A127858 -id:A127858 - cp's OEIS frontend

A127859 a(n) = r(A127858(n)), where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.

7, 79, 943, 11311, 135727, 1628719, 19544623, 234535471, 2814425647, 33773107759, 405277293103, 4863327517231, 58359930206767, 700319162481199, 8403829949774383, 100845959397292591, 1210151512767511087

Offset: 1

Walter Kehowski, Feb 04 2007

In base 12 the sequence is 7, 67, 667, 6667, 66667, 666667, 6666667, 66666667, 666666667, 6666666667.

			a(2)=66 since, in base 12, 66=56, r(56)=67 and r(56^2)=r(2630)=3741=67^2.
In base 12, a(2)=r(A127858(2))=r(56)=67. In base 10, 67 is 79.

Cf. A117755, A127856, A127857, A127858, A127860, A127861, A192544.

a(n) = 6*(12^n - 1)/11 + 1. - Max Alekseyev, Jul 27 2023

More terms from Max Alekseyev, Jul 27 2023

A127860 a(n) = A127858(n)^2.

Original entry on oeis.org

36, 4356, 617796, 88849476, 12792967236, 1842170994756, 265272427798596, 38199227257643076, 5500688696956346436, 792099172023982809156, 114062280767400751587396, 16424968430457074953412676

Offset: 1

Walter Kehowski, Feb 04 2007

In base 12 the sequence is 30, 2630, 259630, 25909630, 2590409630, 259037409630, 259036X7409630, 259036X1X7409630, 259036X151X7409630, 259036X14851X7409630, where X is 10 and E is 11.

			a(1) = A127858(1)^2 = 6^2 = 36.

Cf. A117755, A127856, A127857, A127858, A127859, A127861, A192544.

a(n) = (5*(12^n - 1)/11 + 1)^2 = A127861(n) - (12^(2*n) - 1)/11.. - Max Alekseyev, Jul 27 2023

Edited by Max Alekseyev, Jul 27 2023

A127856 Positive integers n such that if n is a square, then so is r(n), where r(n) is the nonnegative integer defined by cyclic replacement of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.

Original entry on oeis.org

36, 4356, 617796, 910116, 2090916, 4588164, 39463524, 88849476, 173132964, 262245636, 266146596, 1404000900, 12792967236, 1491969417444, 1842170994756, 1904449680324, 7504323317604, 11853326293956, 265272427798596

Offset: 1

Walter Kehowski, Feb 04 2007

			a(1)=36 since 36=30 in base 12 and r(30)=41=7^2.
The only known element starting with the base-12 digit 11 (i.e., turning into a smaller square under the cyclic increments of the digits) is 549014564071245547886724. [From _Max Alekseyev_, Oct 24 2008]

Max Alekseyev, Table of n, a(n) for n=1..62

Cf. A117755, A127857, A127858, A127859, A127860, A127861.

A127857 a(n)=sqrt(A127856(n)).

Original entry on oeis.org

6, 66, 786, 954, 1446, 2142, 6282, 9426, 13158, 16194, 16314, 37470, 113106, 1221462, 1357266, 1380018, 2739402, 3442866, 16287186, 39360078, 72999726, 138846414, 175958202, 195446226, 228662046, 319612062, 355291902, 1200435786

Offset: 1

Walter Kehowski, Feb 04 2007

			a(1)=sqrt(A127856(1))=sqrt(36)=6.

Max Alekseyev, Table of n, a(n) for n = 1..62.

Cf. A117755, A127856, A127858, A127859, A127860, A127861.

Extended by Max Alekseyev, Feb 13 2009

Extended and b-file provided by Max Alekseyev, Feb 13 2009

A127861 a(n) = A127859(n)^2.

Original entry on oeis.org

49, 6241, 889249, 127938721, 18421818529, 2652725580961, 381992288212129, 55006887157191841, 7920991722491368609, 1140622807701026002081, 164249684304894971368609, 23651954539856242601907361

Offset: 1

Walter Kehowski, Feb 04 2007

In base 12 the sequence is 41, 3741, 36X741, 36X1X741, 36X151X741, 36X14851X741, 36X147E851X741, 36X147E2E851X741, 36X147E262E851X741, 36X147E25962E851X741, where X is 10 and E is 11.

			a(1) = A127859(1)^2 = 7^2 = 49.

Cf. A117755, A127856, A127857, A127858, A127859, A127860, A192544.

a(n) = (6*(12^n - 1)/11 + 1)^2 = A127860(n) + (12^(2*n) - 1)/11. - Max Alekseyev, Jul 27 2023

Edited by Max Alekseyev, Jul 27 2023

A173535 a(n) = (1/11) * (5*12^n + 6).

Original entry on oeis.org

1, 6, 66, 786, 9426, 113106, 1357266, 16287186, 195446226, 2345354706, 28144256466, 337731077586, 4052772931026, 48633275172306, 583599302067666, 7003191624811986, 84038299497743826, 1008459593972925906, 12101515127675110866

Offset: 0

Vincenzo Librandi, Nov 23 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (13, -12).

Essentially the same as A127858.

[(1/11)*(5*12^n + 6): n in [0..20]]; // Vincenzo Librandi, Sep 28 2013

Table[(1/11) (5 12^n + 6), {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 7 x)/((1 - x) (1 - 12 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 28 2013 *)

a(n) = 12*a(n-1) - 6, a(0)=1.

G.f.: (1-7*x)/((1-x)*(1-12*x)). - Vincenzo Librandi, Sep 28 2013

Changed offset from 1 to 0 by, added 1 by Vincenzo Librandi, Sep 28 2013

cp's OEIS Frontend

A127859 a(n) = r(A127858(n)), where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.

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A127860 a(n) = A127858(n)^2.

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A127856 Positive integers n such that if n is a square, then so is r(n), where r(n) is the nonnegative integer defined by cyclic replacement of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.

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A127857 a(n)=sqrt(A127856(n)).

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A127861 a(n) = A127859(n)^2.

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A173535 a(n) = (1/11) * (5*12^n + 6).

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