A135770 Numbers whose square is such that another square can be obtained by a cyclic permutation of the digits (excluding leading zeros).

12, 14, 16, 21, 25, 31, 108, 122, 128, 129, 192, 196, 216, 221, 245, 247, 258, 294, 408, 463, 465, 486, 522, 604, 661, 694, 789, 804, 918, 933, 948, 981

Offset

1,1

Comments

This is a subsequence of { sqrt(A034289(n)) }, or equivalently, { a(n)^2 } is a subsequence of A034289. Cf. A135780 for more remarks.

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = sqrt(A135780(n)).

Example

a(1) = 12 since 12^2 = 144 is the least square such that a cyclic permutation of its decimal digits is again a square, namely 441 = 21^2. See A135780 for more explanations.

Prog

(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)", ")))

Crossrefs

Cf. A135780 (the squares), A034289 (allowing arbitrary permutations).

Sequence in context: A163622 A159251 A208156 * A091989 A381501 A078417

Adjacent sequences: A135767 A135768 A135769 * A135771 A135772 A135773

Keyword

base,easy,nonn

Author

M. F. Hasler, following ideas from David W. Wilson, Jan 31 2008

Status

approved