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A382766 Odd primes p such that p + 4, p + 6 and p + 8 are composite.

%I A382766 #42 May 29 2025 06:28:36
%S A382766 113,137,139,179,181,197,199,211,239,241,281,283,293,317,337,409,419,
%T A382766 421,467,509,521,523,547,577,617,619,631,659,661,691,709,773,787,797,
%U A382766 809,811,827,829,839,863,887,919,953,997,1019,1021,1039,1049,1051,1069
%N A382766 Odd primes p such that p + 4, p + 6 and p + 8 are composite.
%H A382766 Robert Israel, <a href="/A382766/b382766.txt">Table of n, a(n) for n = 1..10000</a>
%p A382766 P:= select(isprime,{seq(i,i=3..10008,2)}):
%p A382766 R:= P minus (P -~ 4) minus (P -~ 6) minus (P -~ 8):
%p A382766 sort(convert(R,list)); # _Robert Israel_, Apr 28 2025
%t A382766 Select[Table[
%t A382766   Module[{p = 2, q},
%t A382766    While[True, q = 2 n - p; If[PrimeQ[p] && PrimeQ[q], Break[]];
%t A382766     p = NextPrime[p]]; If[p == 11, q, Nothing]], {n, 2, 1000}], # =!=
%t A382766    Nothing &]
%o A382766 (PARI) isok(p) = (p%2) && isprime(p) && !isprime(p+4) && !isprime(p+6) && !isprime(p+8); \\ _Michel Marcus_, Apr 07 2025
%Y A382766 Cf. A382765, A083371, A124582, A049591, A067774.
%K A382766 nonn
%O A382766 1,1
%A A382766 _Michel Eduardo Beleza Yamagishi_, Apr 04 2025