

A252655


Smallest prime p with property that the sum of the nth power of the successive gaps between primes <= p is also a prime number.


2



5, 5, 7, 5, 43, 13, 7, 5, 241, 13, 43, 41, 19, 41, 7, 5, 13, 83, 43, 229, 811, 41, 31, 167, 811, 127, 367, 419, 79, 43, 43, 83, 673, 19, 109, 83, 13, 331, 523, 409, 199
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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

Abhiram R Devesh and 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=npp
............p=np


CROSSREFS

Cf. A006512, A247177, A247178, A251623.
Sequence in context: A195380 A139261 A247649 * A021646 A231589 A133888
Adjacent sequences: A252652 A252653 A252654 * A252656 A252657 A252658


KEYWORD

nonn


AUTHOR

Abhiram R Devesh, Dec 19 2014


STATUS

approved



