

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
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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)
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*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



