

A135770


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


1



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
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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 A078417 A107835
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



