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 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. 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 (list; graph; refs; listen; history; text; internal format)
 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=np-p ............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

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Last modified December 12 14:12 EST 2018. Contains 318063 sequences. (Running on oeis4.)