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A239733
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Primes p such that 4p+9 and 9p+4 are both prime.
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1
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7, 11, 23, 37, 41, 67, 71, 97, 113, 137, 163, 191, 197, 263, 307, 317, 401, 421, 491, 617, 653, 683, 727, 823, 881, 883, 907, 947, 953, 967, 1031, 1087, 1103, 1217, 1231, 1297, 1451, 1493, 1523, 1567, 1693, 1747, 1933, 1973, 2053, 2141, 2207, 2221, 2281, 2293
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OFFSET
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1,1
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COMMENTS
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All numbers in this sequence are either 1, 3, or 7 mod 10.
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LINKS
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EXAMPLE
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7 is prime, 4*7+9 = 37 is prime, and 9*7+4 = 67 is prime. Thus, 7 is a member of this sequence.
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MATHEMATICA
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Select[Prime[Range[400]], AllTrue[{4#+9, 9#+4}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 26 2014 *)
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PROG
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(Python)
import sympy
from sympy import isprime
{print(n) for n in range(5000) if isprime(4*n+9) and isprime(9*n+4) and isprime(n)}
(PARI) s=[]; forprime(p=2, 3000, if(isprime(4*p+9) && isprime(9*p+4), s=concat(s, p))); s \\ Colin Barker, Mar 26 2014
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CROSSREFS
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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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