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%I #7 Aug 01 2023 17:48:28
%S 12,14,16,21,25,31,108,122,128,129,192,196,216,221,245,247,258,294,
%T 408,463,465,486,522,604,661,694,789,804,918,933,948,981
%N Numbers whose square is such that another square can be obtained by a cyclic permutation of the digits (excluding leading zeros).
%C This is a subsequence of { sqrt(A034289(n)) }, or equivalently, { a(n)^2 } is a subsequence of A034289. Cf. A135780 for more remarks.
%F a(n) = sqrt(A135780(n)).
%e 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.
%o (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)",")))
%Y Cf. A135780 (the squares), A034289 (allowing arbitrary permutations).
%K base,easy,nonn
%O 1,1
%A _M. F. Hasler_, following ideas from _David W. Wilson_, Jan 31 2008
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