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
Offset: 1
Keywords
Examples
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.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 100 terms from Abhiram R Devesh)
Programs
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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 *) -
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
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