A103751 Squares whose digits are all positive and even.

4, 64, 484, 4624, 8464, 26244, 28224, 68644, 228484, 446224, 824464, 868624, 2862864, 8282884, 8868484, 22448644, 26646244, 44462224, 82228624, 82664464, 222248464, 284866884, 662444644, 866242624, 4246868224, 4444622224, 6266622244, 6282464644, 6668682244, 8264264464, 8268628624

Offset

1,1

Comments

Subset of A030098.

All terms end with 4, because when k^2 ends with 6, the tens digit of k^2 is always odd. - Bernard Schott, May 02 2022

The sequence is infinite because squares of the form 4 = 2^2, 64 = 8^2, 4624 = 68^2, 446224 = 668^2, 44462224 = 6668^2, ... (2*(10^k + 2) / 3 )^2 , k >= 0, are terms. - Marius A. Burtea, May 02 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..4198 (terms 1..180 from Marius A. Burtea)

Maple

a:=proc(n) if convert(convert((n^2), base, 10), set) subset {2, 4, 6, 8} then n^2 else fi end:seq(a(n), n=1..100000);

Mathematica

pevQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&And@@EvenQ[idn]]; Select[Range[70000]^2, pevQ] (* Harvey P. Dale, Jul 19 2013 *)

Prog

(PARI) isok(n) = my(d=digits(n)); vecmin(d) && (#select(x->(x%2), d) == 0);
lista(nn) = {my(list = List()); for (n=1, nn, if (isok(n^2), listput(list, n^2); ); ); Vec(list); } \\ Michel Marcus, May 02 2022
(Magma) [n:n in [s*s:s in [1..100000]]| Set(Intseq(n)) subset {2, 4, 6, 8}]; // Marius A. Burtea, May 02 2022

Crossrefs

Cf. A030098.

Sequence in context: A030098 A087045 A169801 * A053959 A343725 A195800

Adjacent sequences: A103748 A103749 A103750 * A103752 A103753 A103754

Keyword

nonn,base

Author

Emeric Deutsch, Mar 28 2005

Extensions

More terms from Bernard Schott, May 02 2022

Status

approved