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A297306
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Primes p such that q = 4*p+1 and r = (2*p+1)/3 are also primes.
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1
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7, 43, 79, 163, 673, 853, 919, 1063, 1429, 1549, 1663, 2143, 2683, 3229, 3499, 4993, 5119, 5653, 5779, 6229, 6343, 7333, 7459, 7669, 8353, 8539, 8719, 9829, 10009, 10243, 10303, 11383, 11689, 12583, 13399, 14149, 14653, 14923, 15649, 16603, 17053, 17389, 17749
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OFFSET
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1,1
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COMMENTS
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This sequence was suggested by Moshe Shmuel Newman. It has its source in his study of finite groups.
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LINKS
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EXAMPLE
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Prime p = 7 is in the sequence because q = 4*7+1 = 29 and r = (2*7+1)/3 = 5 are also primes.
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MAPLE
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a:= proc(n) option remember; local p; p:= `if`(n=1, 1, a(n-1));
do p:= nextprime(p); if irem(p, 3)=1 and
isprime(4*p+1) and isprime((2*p+1)/3) then break fi
od; p
end:
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MATHEMATICA
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a[n_] := a[n] = Module[{p}, p = If[n == 1, 1, a[n-1]]; While[True, p = NextPrime[p]; If[Mod[p, 3] == 1 && PrimeQ[4p+1] && PrimeQ[(2p+1)/3], Break[]]]; p];
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PROG
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(PARI) isok(p) = isprime(p) && isprime(4*p+1) && iferr(isprime((2*p+1)/3), E, 0); \\ Michel Marcus, Nov 27 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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EXTENSIONS
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STATUS
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approved
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