OFFSET
1,1
COMMENTS
First appearance of p, by power, beginning with 5: 1, 3, ??, 6, ??, 13, ??, 86, 23, ??, 12, 5, ... . - Robert G. Wilson v, Jan 11 2015
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 100 terms from Abhiram R Devesh)
EXAMPLE
n=1: p=5; primes less than or equal to 5: [2, 3, 5]; prime gaps: [1, 2]; sum of prime gaps: 3.
n=2: p=5; primes less than or equal to 5: [2, 3, 5]; squares of prime gaps: [1, 4]; sum of squares of prime gaps: 5.
n=3: p=7; primes less than or equal to 7: [2, 3, 5, 7]; cubes of prime gaps: [1, 8, 8]; sum of cubes of prime gaps: 17.
n=4: p=5; primes less than or equal to 5: [2, 3, 5]; 4th power of prime gaps: [1, 16]; sum of 4th power of prime gaps: 17.
MATHEMATICA
f[n_] := Block[{p = 2, s = 0}, While[ !PrimeQ@ s, q = NextPrime@ p; s = s + (q - p)^n; p = q]; p]; Array[f, 60] (* Robert G. Wilson v, Jan 11 2015 *)
PROG
(Python)
import sympy
c=1
while c>0:
....p=2
....d=0
....s=0
....while p>0:
........s=s+(d**c)
........sp=sympy.isprime(s)
........if sp ==True:
............print(c, p)
............p=-1
............c=c+1
........else:
............np=sympy.nextprime(p)
............d=np-p
............p=np
CROSSREFS
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, Dec 19 2014
STATUS
approved