A269588 Numbers n such that n^2 ends with the digits of n reversed (A004086(n)).

1, 5, 6, 963, 9867, 65766, 69714, 6317056, 90899553, 169605719, 4270981082, 96528287587, 465454256742, 692153612536, 182921919071841, 655785969669834, 650700037578750084, 125631041500927357539, 673774165549097456624, 16719041449406813636569

Offset: 1

Author

José Eduardo Gaboardi de Carvalho, Mar 01 2016

Keywords

• nonn
• base

Comments

a(29)>10^32 (if it exists)

Examples

			6317056^2 = 39905196507136 which ends with 6507136, so 6317056 is a term.
		

Links

• Robert Gerbicz, Table of n, a(n) for n = 1..28
• IBM, "Ponder This" puzzle for March 2016

Crossrefs

Subsequence of A115761.

Cf. A003226, A004086.

Programs

Mathematica

Select[Range[10^7], Function[k, Take[IntegerDigits[#^2], -Length@ k] == Reverse@ k]@ IntegerDigits@ # &] (* Michael De Vlieger, Mar 04 2016 *)

PARI

isA269588(n)=dn = digits(n); rn = subst(Polrev(dn), x, 10); nbd = #dn; (n^2 - rn) % 10^nbd == 0; \\ Michel Marcus, Mar 01 2016

PARI

\\ printA269588len(d) prints all terms of the sequence with d digits
rev(n) = eval(concat(Vecrev(Str(n))));
{ printA269588len(d) = my(l, u, n); l=ceil(d/2); u=floor(d/2); for(y=0, 10^l-1, n=rev(y^2 % 10^u)*10^l+y; if(#Str(n)==d && Mod(n, 10^d)^2==rev(n), print(n)); ); }
\\ Max Alekseyev, Mar 07 2016

Extensions

a(18)-a(20) from Max Alekseyev, Mar 07 2016

a(21)-a(27) from Robert Gerbicz, Apr 03 2016

a(28) from Dieter Beckerle, Jun 09 2016