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 A297306 Primes p such that q = 4*p+1 and r = (2*p+1)/3 are also primes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence was suggested by Moshe Shmuel Newman. It has its source in his study of finite groups. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE Prime p = 7 is in the sequence because q = 4*7+1 = 29 and r = (2*7+1)/3 = 5 are also primes. MAPLE 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: seq(a(n), n=1..50);  # Alois P. Heinz, Jan 07 2018 MATHEMATICA 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]; Array[a, 50] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *) PROG (PARI) isok(p) = isprime(p) && isprime(4*p+1) && iferr(isprime((2*p+1)/3), E, 0); \\ Michel Marcus, Nov 27 2020 CROSSREFS Cf. A000040. Intersection of A023212 and A104163. Sequence in context: A052029 A168026 A142102 * A247949 A031914 A172469 Adjacent sequences:  A297303 A297304 A297305 * A297307 A297308 A297309 KEYWORD nonn AUTHOR David S. Newman, Jan 04 2018 EXTENSIONS More terms from Alois P. Heinz, Jan 07 2018 STATUS approved

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Last modified May 23 18:08 EDT 2022. Contains 353993 sequences. (Running on oeis4.)