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A061843 Squares which remain squares if you increment every digit by 1. 1
0, 25, 2025, 13225, 4862025, 60415182025, 207612366025, 153668543313582025, 13876266042653742025, 20761288044852366025, 47285734107144405625, 406066810454367265225, 141704161680410868660551655625 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..13.

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

Cf A002275, A061843.

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

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.