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A135770
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Numbers whose square is such that another square can be obtained by a cyclic permutation of the digits (excluding leading zeros).
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1
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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
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1,1
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COMMENTS
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This is a subsequence of { sqrt(A034289(n)) }, or equivalently, { a(n)^2 } is a subsequence of A034289. Cf. A135780 for more remarks.
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LINKS
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FORMULA
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EXAMPLE
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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.
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PROG
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(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)", ")))
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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