A115975 Numbers of the form p^k, where p is a prime and k is a Fibonacci number.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233

Offset: 1

Author

Giovanni Teofilatto, Mar 15 2006; corrected Apr 23 2006

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A000961 (powers of primes).

Cf. A117245 (partial sums).

Subsequences: A000040, A001248, A030078, A050997, A138031, A179645.

Programs

Mathematica

With[{nn=60},Take[Join[{1},Union[First[#]^Last[#]&/@Union[Flatten[ Outer[List,Prime[Range[nn]],Fibonacci[Range[nn/6]]],1]]]],70]] (* Harvey P. Dale, Jun 05 2012 *)
fib[lim_] := Module[{s = {}, f = 1, k = 2}, While[f <= lim, AppendTo[s, f]; k++; f = Fibonacci[k]]; s]; seq[max_] := Module[{s = {1}, p = 2, e = 1, f = {}}, While[e > 0, e = Floor[Log[p, max]]; If[f == {}, f = fib[e], f = Select[f, # <= e &]]; s = Join[s, p^f]; p = NextPrime[p]]; Sort[s]]; seq[250] (* Amiram Eldar, Aug 09 2024 *)

PARI

{m=240;v=Set([]);forprime(p=2,m,i=0;while((s=p^fibonacci(i))
				

Extensions

Edited and corrected by Klaus Brockhaus, Apr 25 2006