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A256889
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Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 5 as largest digit.
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20
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115, 1115, 1235, 3515, 11115, 12335, 12415, 33515, 35415, 123335, 123512, 124235, 145415, 152132, 231115, 235211, 333515, 1114115, 1155211, 1233335, 1531115, 1534312, 2311115, 3333515, 11114115, 11141115, 11145511, 12333335, 12342335, 15334312, 15531115
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OFFSET
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1,1
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COMMENTS
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k can only begin with 1, 2 or 3 and k mod 10 can only equal 1, 2 or 5. - Robert G. Wilson v, Apr 13 2015
Heuristics suggest that this sequence should be infinite and the sequence with 4 in place of 5 should be finite. The latter sequence contains no terms up to 10^30. - Charles R Greathouse IV, Mar 20 2022
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LINKS
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MATHEMATICA
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fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {6, 10}] == 0, c[[1]] > 0, c[[5]] > 0]]; Select[Range@ 100000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)
fQ[n_] := Block[{id1 = Union@ IntegerDigits[ n], id2 = Union@ IntegerDigits[ n^2]}, Min[id1] == Min[id2] == 1 && Max[id1] == Max[id2] == 5]; k = 1; lst = {}; While[k < 10^7, If[ fQ@ k, AppendTo[lst, k]]; k++; If[ fQ@ k, AppendTo[lst, k]]; k += 3; If[ fQ@ k, AppendTo[lst, k]]; k += 6]; lst (* Robert G. Wilson v, Apr 13 2015 *)
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PROG
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(PARI) is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==5 && vecmax(digits(n^2))==5
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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