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

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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1270

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001359, A006512, A057470, A057473.

Sequence in context: A365786 A365783 A366937 * A220439 A363324 A240620

Adjacent sequences: A096471 A096472 A096473 * A096475 A096476 A096477

Keyword

nonn

Author

Labos Elemer, Jun 23 2004

Status

approved