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Numbers equidistant from consecutive twin prime pairs.
3

%I #21 Jan 02 2020 04:15:04

%S 5,9,15,24,36,51,66,87,105,123,144,165,186,195,213,234,255,276,297,

%T 330,384,426,447,492,546,585,609,630,651,735,816,825,843,870,951,1026,

%U 1041,1056,1077,1122,1191,1254,1284,1296,1311,1374,1440

%N Numbers equidistant from consecutive twin prime pairs.

%H Amiram Eldar, <a href="/A074953/b074953.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A006512(n+1) + A001359(n))/2. - _Michel Marcus_, Jul 26 2015

%e 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.

%t t = Select[ Prime@ Range@ 250, PrimeQ[# + 2] &]; Most@ t + Differences[t]/2 + 1 (* _Robert G. Wilson v_, Jul 26 2015 *)

%o (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

%Y Cf. A001359, A006512.

%K nonn

%O 1,1

%A _Neil Fernandez_, Oct 05 2002