A030159 Numbers n such that in n^3 the parity of digits alternates.

0, 1, 2, 3, 5, 6, 7, 9, 18, 23, 85, 87, 101, 103, 168, 206, 301, 303, 363, 725, 1683, 2461, 2788, 7921, 9563, 9668, 20606, 28443, 29501, 45168, 46701, 49501, 63556, 78206, 80901, 90009, 167861, 168069, 208288, 278636, 331841, 375121, 440468

Offset

1,3

Comments

A simple heuristic argument suggests that this sequence (albeit rather sparse) is infinite. The numbers of terms of k digits, for k=1..14, are 8, 4, 8, 6, 10, 14, 20, 18, 33, 23, 42, 37, 46, 77, respectively. The 5 numbers obtained multiplying the first h=1..5 terms of (1+10^2, 1+10^8, 1+10^32, 1+10^128, 1+10^512), are all member of the sequence. The largest one is a number of 683 digits whose alternating cube has 2047 digits. - Giovanni Resta, Aug 16 2018

Links

Giovanni Resta, Table of n, a(n) for n = 1..350

Mathematica

n3pdaQ[n_]:=Module[{pty=Boole[EvenQ/@IntegerDigits[n^3]], len= IntegerLength[ n^3]}, pty== PadRight[{}, len, {1, 0}]||pty==PadRight[ {}, len, {0, 1}]]; Join[{0}, Select[Range[450000], n3pdaQ]] (* Harvey P. Dale, Mar 26 2018 *)

Crossrefs

Cf. A030160, A030161, A030162, A030151.

Sequence in context: A226808 A096594 A100693 * A030161 A361372 A129125

Adjacent sequences: A030156 A030157 A030158 * A030160 A030161 A030162

Keyword

nonn,base

Author

Patrick De Geest

Status

approved