A251623 Primes p with property that the sum of the 4th powers of the successive gaps between primes <= p is a prime number.

5, 19, 29, 41, 61, 67, 83, 89, 103, 113, 167, 179, 229, 263, 281, 283, 307, 317, 359, 461, 467, 509, 563, 571, 613, 739, 743, 761, 1019, 1031, 1051, 1093, 1229, 1291, 1297, 1319, 1409, 1447, 1609, 1621, 1667, 1747, 1801, 1877, 1979, 2113, 2137, 2161

Offset

1,1

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..1000

Example

a(1)=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.
a(2)=19; primes less than or equal to 13: [2, 3, 5, 7, 11, 13, 17, 19]; 4th powers of prime gaps (see A140299): [1, 16, 16, 256, 16, 256, 16]; sum of these: 577.

Mathematica

p = 2; q = 3; s = 0; lst = {}; While[p < 2500, s = s + (q - p)^4; If[ PrimeQ@ s, AppendTo[lst, q]]; p = q; q = NextPrime@ q]; lst (* Robert G. Wilson v, Dec 19 2014 *)

Prog

(Python)
import sympy
p=2
s=0
while 10000>p>0:
    np=sympy.nextprime(p)
    if sympy.isprime(s):
        print(p)
    d=np-p
    s+=(d**4)
    p=np
(PARI) p = 2; q = 3; s = 1; for (i = 1, 100, p = q; q = nextprime (q + 1); if (isprime (s = s + (q - p)^4), print1 (q ", "))) \\ Zak Seidov, Jan 19 2015

Crossrefs

Cf. A006512 (with gaps), A247177 (with squares of gaps), A247178 (with cubes of gaps).

Sequence in context: A106062 A161891 A296930 * A341079 A045456 A115167

Adjacent sequences: A251620 A251621 A251622 * A251624 A251625 A251626

Keyword

nonn,easy

Author

Abhiram R Devesh, Dec 06 2014

Status

approved