A057609 Powers of a prime lucky number (A031157) but excluding lucky numbers (A000959).

27, 81, 243, 343, 1849, 2197, 2401, 4489, 5329, 6241, 6561, 16129, 16807, 19683, 22801, 26569, 28561, 37249, 44521, 49729, 58081, 59049, 79507, 80089, 94249, 109561, 117649, 134689, 177147, 177241, 187489, 214369, 237169, 361201, 371293, 375769, 383161, 389017

Offset

1,1

Comments

Up to 10^7, terms are 3^3, 3^4, 3^5, 3^8, 3^9, 3^10, 3^11, 3^12, 3^13, 7^3, 7^4, 7^5, 7^6, 13^3, 13^4, 13^5, 13^6, 31^4, 43^2, 43^3, 43^4, 67^2, ..., . - Robert G. Wilson v, May 12 2006

Links

Giovanni Resta, Table of n, a(n) for n = 1..825 (terms < 4*10^9)

Example

In the first 23 terms of A000959, {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99}, 3 is a prime lucky number (A031157), and 3^2 is also a lucky number, but 3^3=27 and 3^4=81 are not lucky numbers, so they are terms of this sequence.

Mathematica

lst = Range[1, 2*10^6, 2]; i = 2; While[i <= (len = Length[lst]) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; m = Last@ lst; Complement[ Reap[ Do[ If[x^2 > m, Break[]]; If[PrimeQ[x], y = x^2; While[y <= m, Sow@ y; y *= x]], {x, lst}]] [[2, 1]], lst] (* Robert G. Wilson v, May 12 2006, corrected by Giovanni Resta, May 10 2020 *)

Crossrefs

Cf. A031157, A000959.

Sequence in context: A215782 A216438 A292872 * A255624 A008884 A031455

Adjacent sequences: A057606 A057607 A057608 * A057610 A057611 A057612

Keyword

nonn

Author

Naohiro Nomoto, Oct 09 2000

Extensions

More terms from Robert G. Wilson v, May 12 2006

Data corrected and extended by Giovanni Resta, May 10 2020

Status

approved