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

Author

Abhiram R Devesh, Nov 22 2014

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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