

A251623


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


3



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
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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 p>0:
....np=sympy.nextprime(p)
....if sympy.isprime(s)==True:
........print(p)
....d=npp
....s=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 * A045456 A115167 A115103
Adjacent sequences: A251620 A251621 A251622 * A251624 A251625 A251626


KEYWORD

nonn,easy


AUTHOR

Abhiram R Devesh, Dec 06 2014


STATUS

approved



