A247177 Primes p with property that the sum of the squares of the successive gaps between primes <= p is a prime number.

5, 13, 29, 41, 89, 97, 139, 173, 179, 263, 269, 281, 307, 337, 353, 431, 439, 461, 487, 499, 509, 569, 607, 613, 641, 643, 661, 709, 739, 761, 809, 823, 839, 857, 919, 941, 967, 991, 1031, 1039, 1061, 1117, 1129, 1163, 1171, 1201, 1229, 1277, 1381, 1399

Offset

1,1

Comments

If A074741(n) is prime, then prime(n+1) is in this sequence. - Michel Marcus, Jan 12 2015

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]; squares of prime gaps: [1, 4]; sum of squares of prime gaps: 5.
a(2)=13; primes less than or equal to 13: [2, 3, 5, 7, 11, 13]; squares of prime gaps: [1, 4, 4, 16, 4]; sum of squares of prime gaps: 29.

Prog

(Python)
from sympy import nextprime, isprime
p = 2
s = 0
while s < 8000:
    np = nextprime(p)
    if isprime(s):
        print(p)
    d = np - p
    s += d*d
    p = np
(PARI) listp(nn) = {my(s = 0); my(precp = 2); forprime (p=3, nn, if (isprime(ns = (s + (p - precp)^2)), print1(p, ", ")); s = ns; precp = p; ); } \\ Michel Marcus, Jan 12 2015

Crossrefs

Cf. A074741 (sum of squares of gaps between consecutive primes).

Sequence in context: A277701 A159351 A163251 * A146286 A065374 A130066

Adjacent sequences: A247174 A247175 A247176 * A247178 A247179 A247180

Keyword

nonn,easy

Author

Abhiram R Devesh, Nov 22 2014

Status

approved