A256889 Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 5 as largest digit.

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

Offset

1,1

Comments

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2000 (n = 1..75 from Robert G. Wilson v).

Mathematica

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 *)

Prog

(PARI) is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==5 && vecmax(digits(n^2))==5

Crossrefs

Cf. A256630, A256631, A256633, A256634, A256708, A256709.

Sequence in context: A218324 A258673 A287430 * A256354 A005466 A279451

Adjacent sequences: A256886 A256887 A256888 * A256890 A256891 A256892

Keyword

base,nonn

Author

Felix Fröhlich, Apr 12 2015

Status

approved