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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)