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

1,2

Links

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

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 *)

Prog

(PARI) {m=240; v=Set([]); forprime(p=2, m, i=0; while((s=p^fibonacci(i))<m, v=setunion(v, Set(s)); i++)); v=vecsort(eval(v)); for(j=1, #v, print1(v[j], ", "))}

Crossrefs

Subsequence of A000961 (powers of primes).

Cf. A117245 (partial sums).

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

Sequence in context: A322546 A283262 A334393 * A277187 A339841 A087797

Adjacent sequences: A115972 A115973 A115974 * A115976 A115977 A115978

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 15 2006; corrected Apr 23 2006

Extensions

Edited and corrected by Klaus Brockhaus, Apr 25 2006

Status

approved