A074953 Numbers equidistant from consecutive twin prime pairs.

5, 9, 15, 24, 36, 51, 66, 87, 105, 123, 144, 165, 186, 195, 213, 234, 255, 276, 297, 330, 384, 426, 447, 492, 546, 585, 609, 630, 651, 735, 816, 825, 843, 870, 951, 1026, 1041, 1056, 1077, 1122, 1191, 1254, 1284, 1296, 1311, 1374, 1440

Offset: 1

Author

Neil Fernandez, Oct 05 2002

Keywords

• nonn

Examples

			The twin prime pairs are (3,5), (5,7), (11,13), (17,19), etc. a(n) is equidistant from the higher prime in the n-th pair and the lower prime in the (n+1)th pair. E.g., a(2) is the mean of 7 and 11, which is 9.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512.

Programs

Mathematica

t = Select[ Prime@ Range@ 250, PrimeQ[# + 2] &]; Most@ t + Differences[t]/2 + 1 (* Robert G. Wilson v, Jul 26 2015 *)
Mean/@Partition[Rest[Flatten[Select[Partition[Prime[Range[250]],2,1],#[[2]]-#[[1]]==2&]]],2] (* Harvey P. Dale, Mar 01 2025 *)

PARI

lista(nn) = {forprime (p=2, nn, q = nextprime(p+1); if (q==p+2, forprime (pp=q, nn, if (nextprime(pp+1) == pp+2, print1((q+pp)/2, ", "); break;););););} \\ Michel Marcus, Jul 26 2015

Formula

a(n) = (A006512(n+1) + A001359(n))/2. - Michel Marcus, Jul 26 2015