What comes next in this kinda-numerical sequence:

===================




6105
77156
948717
==================

Yes, the first four of the entries are blank.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

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On 5/17/2025 4:03 AM, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

===================

6105
77156
948717
==================

Yes, the first four of the entries are blank.

Phil

Are you sure that the last number shouldn't be 948617? If it is 948617,
then 2324788 may come next.
--
Carl G.


--
This email has been checked for viruses by AVG antivirus software.
www.avg.com

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"Carl G." <carlgnews@microprizes.com> writes:

On 5/17/2025 4:03 AM, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

===================




6105
77156
948717
==================

Yes, the first four of the entries are blank.

Are you sure that the last number shouldn't be 948617? If it is
948617, then 2324788 may come next.

Now you have me intrigued! However, the 7th term is indeed 948717.
As an extra pointer, the subsequent terms become incredibly predictable
very quickly at this point, until you hit the 25th term.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

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On Sat, 17 May 2025 14:03:03 +0300, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

Hello Phil,

Would you care to post a pointer, or a solution with the usual
obscuration?

I can't see any numerical connection, but that certainly doesn't mean
there isn't one.

--
David Entwistle

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David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> writes:

On Sat, 17 May 2025 14:03:03 +0300, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

Hello Phil,

Would you care to post a pointer, or a solution with the usual
obscuration?

It's been long enough, here's the answer:

214358881

That might be enough to give the rule away, but if not, here's a
rot-13 explanation:

Gurl ner gur aba-cnyvaqebzvp cnegf bs gur cbjref bs 11 va onfr gra.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

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On Sat, 17 May 2025 14:03:03 +0300, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

Sort of related to the original question...

1, 2, 4, 8, 7, ?

Ubcr V unir guvf evtug... Svir. Gurl ner gur qvtvgny ebbg (gur fhz bs gur qvtvgf) va gur frevrf bs ryrira envfrq gb gur cbjre mreb, bar, gjb rgp.
Sbe gubfr jub yvxr fhpu guvatf, jul vf vg gur fnzr nf gur fhz bs gur
qvtvgf va gur frevrf bs gjb envfrq gb gur cbjre mreb, bar, gjb rgp.

--
David Entwistle

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On Mon, 30 Jun 2025 12:03:27 +0300, Phil Carmody wrote:

It's been long enough, here's the answer:

Ah, very good. If I had realized it was such a reasonably structured
question, I may have tried harder. However, I doubt I would have had the insight to find the solution. I'll have a better understanding of the type
of question you may pose, when I see future posts from you.

Best wishes,
--
David Entwistle

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Phil Carmody <pc+usenet@asdf.org> posted:

"Carl G." <carlgnews@microprizes.com> writes:

On 5/17/2025 4:03 AM, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

===================
(blank)
(blank)
(blank)
(blank)
6105
77156
948717
==================

Yes, the first four of the entries are blank.

Are you sure that the last number shouldn't be 948617? If it is
948617, then 2324788 may come next.

What's the thinking here?

Now you have me intrigued! However, the 7th term is indeed 948717.
As an extra pointer, the subsequent terms become incredibly predictable
very quickly at this point, until you hit the 25th term.

Phil

--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in The Western Tradition



What's the thinking here?

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David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> writes:

On Sat, 17 May 2025 14:03:03 +0300, Phil Carmody wrote:

What comes next in this kinda-numerical sequence:

Sort of related to the original question...

1, 2, 4, 8, 7, ?

Ubcr V unir guvf evtug... Svir. Gurl ner gur qvtvgny ebbg (gur fhz bs gur qvtvgf) va gur frevrf bs ryrira envfrq gb gur cbjre mreb, bar, gjb rgp.
Sbe gubfr jub yvxr fhpu guvatf, jul vf vg gur fnzr nf gur fhz bs gur
qvtvgf va gur frevrf bs gjb envfrq gb gur cbjre mreb, bar, gjb rgp.

Because 1+1=2!

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

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On Tue, 22 Jul 2025 22:06:42 +0300, Phil Carmody wrote:

Because 1+1=2!

Is that it?

I was thinking more along the lines of the following, where DR is the
digital root (the sum of the digits repeated until you get to a single
digit), why are these two sequences the same?

2^0 = 1, DR = 1
2^1 = 2, DR = 2
2^2 = 4, DR = 4
2^3 = 8, DR = 8
2^4 = 16, DR = 7
2^5 = 32, DR = 5
2^6 = 64, DR = 1
2^7 = 128, DR = 2

11^0 = 1, DR = 1
11^1 = 11, DR = 2
11^2 = 121, DR = 4
11^3 = 1331, DR = 8
11^4 = 14641, DR = 7
11^5 = 161051, DR = 5
11^7 = 1771561, DR = 1
11^7 = 19487171, DR = 2

I'm thinking it's because the digital root is a Mod(9) calculation and 11
% 9 = 2. But I may be losing the plot.

--
David Entwistle

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On Tue, 22 Jul 2025 22:06:42 +0300, Phil Carmody wrote:

Because 1+1=2!

On reflection, I see that is the reason. I've been over-thinking it and
not fully understanding the fundamentals.

Thanks.

--
David Entwistle

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On Thu, 24 Jul 2025 05:32:47 -0000 (UTC), David Entwistle wrote:

On reflection, I see that is the reason. I've been over-thinking it and
not fully understanding the fundamentals.

Or, possibly not. I'm feeling a little fragile at the moment and I need to think about this. It's all good, only numbers and a bit of a puzzle,
should be fun.

--
David Entwistle

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