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

Author

Emeric Deutsch, Mar 28 2005

Keywords

• nonn
• base

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)

Crossrefs

Cf. A030098.

Programs

Magma

[n:n in [s*s:s in [1..100000]]| Set(Intseq(n)) subset {2,4,6,8}]; // Marius A. Burtea, May 02 2022

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 *)

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

Extensions

More terms from Bernard Schott, May 02 2022