1,1

This is a subsequence of A034289.

It seems that there are never more than two squares having the same digits up to a cyclic permutation (checked up to (10^8)^2).

M. F. Hasler, Table of n, a(n) for n = 1..816

a(1) = 144 = 12^2 is the least square such that a cyclic permutation of its decimal digits is again a square, namely 441 = 21.

a(2) = 196 = 14^2 is the second least square having this property, with 961 = 19^2.

A034289(2)=169 does not figure here, since the permutations of its digits yielding squares are 196 and 961, which are not cyclic permutations of 169.

The number 25600 is here since 60025 is also a square.

The fact that 00256 also is a square is irrelevant: permutations with leading zeros are not considered.

(PARI) for(n=1, 10^8, (t=n^2)/* %10|next <= this would exclude terms with trailing '0's */; found=0; for(j=1, k=#Str(t)-1, t=divrem(t, 10); t[2]|(t=t[1])&next /* <= this excludes leading '0's */; issquare(t=t[1]+10^k*t[2])|next; /* t%10|next; <= would exclude permutations with trailing '0's */ print1( if(found, "<<<"/* mark multiple permutations: this never happens */, found=1; n^2)", ")))

Cf. A034289 (allowing arbitrary permutations), A135770.

Sequence in context: A156316 A165076 A165078 this_sequence A069701 A124144 A061040

Adjacent sequences: A135777 A135778 A135779 this_sequence A135781 A135782 A135783

base,easy,nonn,nice

David W. Wilson (wilson.d(AT)anseri.com) and M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 09 2008