A345399 a(n) is the least number k such that {k, k^2, ..., k^n} are all odious numbers (A000069), but k^(n+1) is not.

13, 7, 25, 59, 193, 313, 1447, 103, 2431, 1305, 29089, 21117, 10525, 26663, 63271, 25127, 106501, 215735, 1143579, 5115041, 810163, 9554677, 23932393, 13101403, 14299679, 62266699, 739155479, 37795511, 4015916137, 3197105709, 5386711727, 14904706741, 20696039773

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Example

13 is a term since it is an odious number (13 = 1101_2 has 3 1's), but 13^2 = 169 is not (169 = 10101001_2 has 4 1's), and 13 is the least number with this property.

Mathematica

odQ[n_] := n > 1 && OddQ[n]; odiousQ[n_] := odQ @ DigitCount[n, 2, 1]; f[n_] := Module[{e = 0, r = n}, While[odiousQ[r], r *= n; e++]; e]; m = 15; s = Table[0, {m}]; c = 0; n = 1; While[c < m, k = f[n]; If[0 < k <= m && s[[k]] == 0, c++; s[[k]] = n]; n++]; s

Crossrefs

Cf. A000069, A345398.

Sequence in context: A364091 A257928 A206611 * A298257 A298928 A152142

Adjacent sequences: A345396 A345397 A345398 * A345400 A345401 A345402

Keyword

nonn,base

Author

Amiram Eldar, Jun 17 2021

Status

approved