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

%I

%S 0,25,2025,13225,4862025,60415182025,207612366025,153668543313582025,

%T 13876266042653742025,20761288044852366025,47285734107144405625,

%U 406066810454367265225,141704161680410868660551655625

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

%C 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

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

%o (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

%Y Cf. A002275, A061843.

%K base,nonn

%O 1,2

%A _Erich Friedman_, Jun 23 2001

%E More terms from _Franklin T. Adams-Watters_, May 25 2006

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Last modified August 16 22:14 EDT 2022. Contains 356169 sequences. (Running on oeis4.)