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

%I A061843 #24 Jun 30 2025 20:45:32
%S A061843 0,25,2025,13225,4862025,60415182025,207612366025,153668543313582025,
%T A061843 13876266042653742025,20761288044852366025,47285734107144405625,
%U A061843 406066810454367265225,141704161680410868660551655625
%N A061843 Squares which remain squares if you increment every digit by 1.
%C A061843 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
%H A061843 Max Alekseyev, <a href="/A061843/b061843.txt">Table of n, a(n) for n = 1..78</a> (contains all terms below 10^262)
%e A061843 13225 = 115^2 and 24336 = 156^2.
%t A061843 Select[Range[0,500000]^2,With[{lst=IntegerDigits[#]+1},Max[lst]<10&&IntegerQ[Sqrt[FromDigits[lst]]]&]] (* The program generates the first 7 terms of the sequence. *)  (* _Harvey P. Dale_, Jan 26 2025 *)
%o A061843 (PARI) hasdigit(n, d, b=10) = local(r); r=0;while(r==0&&n>=1,if(n%b==d,r=1,n\=b));r
%o A061843 /* Generates all positive n-digit solutions (in reverse order) */
%o A061843 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 A061843 Subsequence of A117755.
%Y A061843 Cf. A002275, A061844.
%K A061843 base,nonn
%O A061843 1,2
%A A061843 _Erich Friedman_, Jun 23 2001
%E A061843 More terms from _Franklin T. Adams-Watters_, May 25 2006