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%I #46 Sep 08 2022 08:46:24
%S 23,37,53,67,83,97,113,127,263,277,293,307,353,367,383,397,443,457,
%T 563,577,593,607,743,757,773,787,863,877,953,967,983,997,1103,1117,
%U 1223,1237,1283,1297,1433,1447,1553,1567,1583,1597,1613,1627
%N Prime pairs of the form (30k - 7, 30k + 7).
%C The terms of this sequence are created by pairing the terms of the primes when the terms 30k - 7 and 30k + 7 are both prime. As has been pointed out, it is only a guess as to whether, or not, that (like the twin primes, etc.) there is or is not an infinite number of these pairings.
%e As 4 * 30 - 7 = 113 and 4 * 30 + 7 = 127 are prime, both 113 and 127 are in the sequence. - _David A. Corneth_, Nov 10 2019
%t Select[Prime[Range[1000]], MemberQ[{7, 23}, Mod[#, 30]] &] (* _Jinyuan Wang_, Nov 16 2019 *)
%t Flatten[Select[Table[30n + {-7, 7}, {n, 90}], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &]] (* _Alonso del Arte_, Dec 07 2019 *)
%o (PARI) first(n) = n+=(n%2); my(res=List(),todo=n); for(i=1,oo, if(isprime(30*i-7) && isprime(30*i+7), listput(res,30*i-7); listput(res,30*i+7); todo-=2; if(todo<=0, return(res)))) \\ _David A. Corneth_, Nov 10 2019
%o (Magma) &cat[[30*k-7] cat [30*k+7]:k in [1..60]|IsPrime(30*k-7) and IsPrime(30*k+7)]; // _Marius A. Burtea_, Nov 17 2019
%Y Cf. A140446, A153417, A007510.
%Y Odd- (resp. even-) indexed terms are a subsequence of A132235 (resp. A132231).
%K nonn,tabf
%O 1,1
%A _Harry E. Neel_, Nov 09 2019
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