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%I #40 Sep 06 2023 13:41:07
%S 1,2,3,4,9,10,12,13,15,19,20,25,26,29,32,33,37,41,43,48,52,53,54,58,
%T 66,67,76,78,81,85,88,89,90,92,95,97,101,107,118,120,121,128,129,134,
%U 143,150,153,155,165,166,172,178,180,194,195,202,207,209,211,212
%N Numbers k > 0 such that 30k +- 7 is prime.
%C Looking for prime factors > 5=prime(3) in 8=A005867(3) candidates mod 30=A002110(3) two candidates in the form 30k +- 7 with k > 0 never belong to a twin prime pair. Twin primes can be (30k-13, 30k-11) A331840, (30k-1, 30k +1) A176114, or (30k+11, 30k+13) A089160.
%H Frank Ellermann, <a href="/A005867/a005867.txt">Illustration for A002110, A005867, A038110, A060753</a>
%e a(4)=4 for prime(30)=113=4*30-7 and prime(31)=127=4*30+7.
%e a(5)=9 for prime(56)=263=9*30-7 and prime(59)=277=9*30+7.
%t Select[Range@ 215, AllTrue[30 # + {-7, 7}, PrimeQ] &] (* _Michael De Vlieger_, Feb 25 2020 *)
%o (Rexx)
%o S = 1
%o do N = 2 while length( S ) < 255
%o if NOPRIME( N * 30 + 7 ) then iterate N
%o if NOPRIME( N * 30 - 7 ) then iterate N
%o S = S || ',' N
%o end N
%o say S
%Y Cf. A000040, A002110, A005867, A089160, A176114, A331840.
%Y Subsequence of A158573. Prime pairs 30k +- 7 in A329262.
%K nonn,easy
%O 1,2
%A _Frank Ellermann_, Feb 25 2020
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