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A247177
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Primes p with property that the sum of the squares of the successive gaps between primes <= p is a prime number.
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4
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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
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A074741 (sum of squares of gaps between consecutive primes).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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