A192544 -id:A192544 - cp's OEIS frontend

A127858 Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.

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

Offset: 1

Walter Kehowski, Feb 04 2007

In base 12 the sequence is 6, 56, 556, 5556, 55556, 555556, 5555556, 55555556, 555555556, 5555555556, and so on.

If r is the cyclic replacement map in base 10, then the only positive integers n with the property that r(n^2)=r(n)^2 appear to be 5, 45. For example, r(45^2)=r(2025)=3136=56^2=r(45)^2.

			a(2)=66 since, in base 12, 66=56, r(56)=67 and r(56^2)=r(2630)=3741=67^2.

Subsequence of A127857.

Cf. A117755, A127856, A127859, A127860, A127861, A192544.

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

Edited by Max Alekseyev, Jul 27 2023

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.

Original entry on oeis.org

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

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

cp's OEIS Frontend

A127858 Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map 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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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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A127861 a(n) = A127859(n)^2.

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