A329262 Prime pairs of the form (30k - 7, 30k + 7).

23, 37, 53, 67, 83, 97, 113, 127, 263, 277, 293, 307, 353, 367, 383, 397, 443, 457, 563, 577, 593, 607, 743, 757, 773, 787, 863, 877, 953, 967, 983, 997, 1103, 1117, 1223, 1237, 1283, 1297, 1433, 1447, 1553, 1567, 1583, 1597, 1613, 1627

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..46.

Example

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

Mathematica

Select[Prime[Range[1000]], MemberQ[{7, 23}, Mod[#, 30]] &] (* Jinyuan Wang, Nov 16 2019 *)
Flatten[Select[Table[30n + {-7, 7}, {n, 90}], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &]] (* Alonso del Arte, Dec 07 2019 *)

Prog

(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
(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

Crossrefs

Cf. A140446, A153417, A007510.

Odd- (resp. even-) indexed terms are a subsequence of A132235 (resp. A132231).

Sequence in context: A179780 A153740 A055114 * A268343 A063643 A361530

Adjacent sequences: A329259 A329260 A329261 * A329263 A329264 A329265

Keyword

nonn,tabf

Author

Harry E. Neel, Nov 09 2019

Status

approved