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A130448
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Squares whose decimal representation contains no proper subsequence which is a positive square.
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5
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1, 4, 9, 25, 36, 576, 676, 7056, 80656, 665856, 2027776, 2802276, 22282727076, 77770707876, 78807087076, 7888885568656, 8782782707776, 72822772707876, 555006880085056, 782280288087076, 827702888070276, 888288787822276, 2282820800707876, 7880082008070276, 80077778877070276, 88778000807227876, 782828878078078276, 872727072820287876
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OFFSET
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1,2
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COMMENTS
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Is this sequence finite and if so what is the last term?
Yes, the sequence must be finite. This follows from a well-known result: there are no infinite antichains for the subsequence ordering. - Jeffrey Shallit, Mar 05 2014
If it exists, a(29) is greater than 10^18. - Mauro Fiorentini, Jan 24 2017
If it exists, a(51) is greater than 2*10^30. - Giovanni Resta, Jan 08 2018
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LINKS
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Martin Raab, Table of n, a(n) for n = 1..55 (terms 1..50 from Giovanni Resta, terms 51..55 from Martin Raab)
Wikipedia, Subsequence
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EXAMPLE
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576 is in the list because none of its proper subsequences 5, 7, 6, 57, 76 or 56 are squares.
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MATHEMATICA
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fQ[n_] := Module[{d = IntegerDigits[n], ds, sq}, ds = FromDigits /@ Union[Most[Rest[Subsets[d]]]]; sq = Select[ds, # > 0 && IntegerQ[Sqrt[#]] &, 1]; sq == {}]; Select[Range[0, 100000]^2, fQ] (* T. D. Noe, Mar 05 2014 *)
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PROG
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(PARI) isok(n) = {my(d = digits(n)); for (k = 1, #d, for (j= 1, #d - k + 1, if (j != #d, sd = vector(j, i, d[k+i-1]); nsd = fromdigits(sd); if (nsd && issquare(nsd), return(0)); ); ); ); return (1); } \\ Michel Marcus, Apr 21 2018
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CROSSREFS
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Cf. A131599, A238334 (substrings).
Sequence in context: A046659 A063760 A238334 * A046451 A341790 A350152
Adjacent sequences: A130445 A130446 A130447 * A130449 A130450 A130451
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KEYWORD
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base,nonn,fini
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AUTHOR
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Martin Raab, Aug 07 2007
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 14 2007
a(23)-a(28) from Mauro Fiorentini, Jan 24 2017
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STATUS
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approved
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