A061843 Squares which remain squares if you increment every digit by 1.

0, 25, 2025, 13225, 4862025, 60415182025, 207612366025, 153668543313582025, 13876266042653742025, 20761288044852366025, 47285734107144405625, 406066810454367265225, 141704161680410868660551655625

Offset

1,2

Comments

Incrementing each digit means b^2-a^2 = R_n, the n-digit repunit (10^n-1)/9; so solutions must be of the form a = (u-v)/2, b = (u+v)/2, where u * v = R_n. It remains to check that this is in the right range and a has no 9's. - Franklin T. Adams-Watters, May 25 2006

Links

Max Alekseyev, Table of n, a(n) for n = 1..78 (contains all terms below 10^262)

Example

13225 = 115^2 and 24336 = 156^2.

Prog

(PARI) hasdigit(n, d, b=10) = local(r); r=0; while(r==0&&n>=1, if(n%b==d, r=1, n\=b)); r /* Generates all positive n-digit solutions (in reverse order) */ A061843s(n) = local(f, nf, v, i, ru, lb, ub, x); lb=10^(n-1); ub=10^n-1; ru=ub\9; f=divisors(ru); v=[]; nf=matsize(f)[2]; for(i=1, nf\2, x=( (f[nf+1-i]-f[i])\2)^2; if(x>=lb&&x<=ub&&!hasdigit(x, 9), v=concat(v, [x]))); v \\ Franklin T. Adams-Watters, May 25 2006

Crossrefs

Subsequence of A117755.

Cf. A002275, A061844.

Sequence in context: A281436 A197671 A051112 * A173948 A279276 A197408

Adjacent sequences: A061840 A061841 A061842 * A061844 A061845 A061846

Keyword

base,nonn

Author

Erich Friedman, Jun 23 2001

Extensions

More terms from Franklin T. Adams-Watters, May 25 2006

Status

approved