A096474 Difference prime(q+2) - prime(q) as q runs through the lesser members of twin primes (A001359).

6, 6, 10, 8, 18, 12, 6, 14, 16, 12, 24, 18, 24, 18, 16, 14, 24, 18, 24, 18, 10, 12, 18, 40, 28, 20, 24, 18, 28, 10, 12, 12, 8, 8, 22, 16, 12, 12, 14, 14, 26, 36, 24, 30, 24, 8, 18, 30, 12, 22, 22, 16, 18, 24, 10, 14, 18, 14, 10, 20, 10, 32, 32, 12, 10, 44, 30, 18, 16, 36, 14, 12

Offset: 1

Author

Labos Elemer, Jun 23 2004

Keywords

• nonn

Examples

			{q, q+2} = {17, 19} is the 4th twin-pair and prime(19) - prime(17) = 67 - 59 = 8, so a(4) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1270 from Vincenzo Librandi)

Crossrefs

Cf. A001359, A006512, A057470, A057473.

Programs

Mathematica

{ta=Table[0, {1300}], tb=Table[0, {1300}], tc=Table[0, {1300}], u=1}; Do[s=Prime[n+1]-Prime[n];If[Equal[s, 2], ta[[u]]=Prime[Prime[n+1]]-Prime[Prime[n]];tb[[u]]=n; tc[[u]]=Prime[n];u=u+1], {n, 1, 10000}];ta
Prime[#[[2]]]-Prime[#[[1]]]&/@Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Dec 26 2023 *)

PARI

lista(nn) = {forprime(q=2, nn, if (isprime(q+2), print1(prime(q+2)-prime(q), ", ")););} \\ Michel Marcus, Jul 27 2017

Formula

a(n) = prime(A006512(n)) - prime(A001359(n)).

a(n) = A057473(n) - A057470(n). - Michel Marcus, Jul 27 2017