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A130448 Squares whose decimal representation contains no proper subsequence which is a positive square. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

576 is in the list because none of its proper subsequences 5, 7, 6, 57, 76 or 56 are squares.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A131599, A238334 (substrings).

Sequence in context: A046659 A063760 A238334 * A046451 A158142 A158143

Adjacent sequences:  A130445 A130446 A130447 * A130449 A130450 A130451

KEYWORD

base,nonn,fini

AUTHOR

Martin Raab, Aug 07 2007

EXTENSIONS

Edited by N. J. A. Sloane, Sep 14 2007

a(23)-a(28) from Mauro Fiorentini, Jan 24 2017

STATUS

approved

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Last modified July 2 08:02 EDT 2020. Contains 335398 sequences. (Running on oeis4.)