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A103751
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Squares whose digits are all positive and even.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MAPLE
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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);
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MATHEMATICA
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pevQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&And@@EvenQ[idn]]; Select[Range[70000]^2, pevQ] (* Harvey P. Dale, Jul 19 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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