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A339917
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Primes p such that p+k and p^2+k are prime, where k = (p^2-1)/6.
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2
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13, 19, 71, 89, 103, 139, 233, 269, 409, 733, 1009, 1201, 1453, 1579, 1601, 1723, 2053, 2143, 2251, 2699, 2753, 3181, 3259, 3271, 3361, 3491, 3739, 3923, 4051, 4159, 4231, 4283, 4483, 4639, 4733, 5059, 5413, 5431, 5449, 6481, 6911, 7069, 7109, 7253, 7523, 7541, 7703, 7723, 7789, 7901, 8209, 9433
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(3) = 71 is a term because with k = (71^2-1)/6 = 840, 71, 71+840 = 911 and 71^2+840 = 5881 are all primes.
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MAPLE
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select(p -> isprime(p) and isprime((7*p^2-1)/6) and isprime((p^2+6*p-1)/6), [seq(seq(6*i+j, j=[1, 5]), i=0..10000)]);
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PROG
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(PARI) isok(p) = isprime(p) && iferr(isprime(p+(p^2-1)/6) && isprime(p^2+(p^2-1)/6), E, 0); \\ Michel Marcus, Dec 23 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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