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%I #22 May 26 2018 08:44:39
%S 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
%U 191,193,197,199,223,227,229,233,239,241,251,257,263,269,271,277,281
%N Primes p such that at least one number among p+-2, p+-4, p+-6 is also a prime.
%C The union of A167833 and this sequence is the set of all prime numbers, A000040.
%H Lei Zhou, <a href="/A240699/b240699.txt">Table of n, a(n) for n = 1..10000</a>
%e Prime number 191: the closest prime number to 191 is 193 with 193-191 = 2 <= 6. So 191 is in this sequence.
%e Prime number 211: the closest prime number to 211 is 199 with 211-199=12 > 6. So 211 is not in this sequence.
%t p = 2; Table[While[p = NextPrime[p]; ((NextPrime[p] - p) > 6) && (6 < (p - NextPrime[p, -1]))]; p, {n, 1, 58}]
%o (PARI) forprime(p=3, 250, if(p-precprime(p-1)<7, print1(p, ", "), if(nextprime(p+1)-p<7, print1(p, ", ")))) \\ _Felix Fröhlich_, Aug 16 2014; corrected by _Michel Marcus_, May 26 2018
%Y Cf. A000040, A167833, A137870.
%K nonn,easy
%O 1,1
%A _Lei Zhou_, Apr 10 2014
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