A252655 Smallest prime p with property that the sum of the n-th power of the successive gaps between primes <= p is also a prime number.

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, 349, 181, 727, 499, 67, 127, 41, 409, 1951, 2647, 19, 1579, 809, 223, 149, 463, 61, 43, 311

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

Cf. A006512, A247177, A247178, A251623.

Sequence in context: A139261 A352442 A247649 * A021646 A394368 A231589

Adjacent sequences: A252652 A252653 A252654 * A252656 A252657 A252658

Keyword

nonn

Author

Abhiram R Devesh, Dec 19 2014

Status

approved