login
A247177
Primes p with property that the sum of the squares of the successive gaps between primes <= p is a prime number.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Nov 22 2014
STATUS
approved