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

Author

Walter Kehowski, Feb 04 2007

Keywords

• nonn
• base

Comments

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.

Examples

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

Crossrefs

Subsequence of A127857.

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

Formula

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

Extensions

Edited by Max Alekseyev, Jul 27 2023