A254033 - OEIS

%I #19 Jun 13 2018 03:27:17

%S 0,1,2,3,6,10,15,20,21,28,37,44,53,76,96,113,123,135,142,150,181,191,

%T 235,270,291,294,313,327,334,395,403,411,445,478,496,539,582,587,654,

%U 693,722,732,757,754,772,778,791,832,830,848,920,930,955,1004,1053,1151,1240

%N Number of primes dividing exactly one number in the next largest gap between primes.

%H Robert G. Wilson v, <a href="/A254033/b254033.txt">Table of n, a(n) for n = 1..75</a>

%e The 5th largest prime gap (after 2-3, 3-5, 7-11 and 23-29) occurs between 89 and 97, and there are 6 primes which occur exactly once in this gap, namely 7 (dividing 91), 13 (dividing 91), 19 (dividing 95), 23 (dividing 92), 31 (dividing 93) and 47 (dividing 94), so a(5)=6.

%t gp = (* the list of primes in A002386 *); f[n_] := Block[{p = gp[[n]], q = NextPrime[ gp[[n]]]}, r = Range[p + 1, q - 1]; lng = Length@ r; t = Split@ Sort@ Flatten@ Table[ First@# & /@ FactorInteger[ r[[i]]], {i, lng}]; Length@ Select[t, Length@# == 1 &]]; Array[f, 75] (* _Robert G. Wilson v_, Jan 23 2015 *)

%Y Sequences related to increasing prime gaps: A005250, A002386, A000101, A005669.

%K nonn

%O 1,3

%A _Mamuka Jibladze_, Jan 23 2015

%E a(43)-a(57) from _Robert G. Wilson v_, Jan 23 2015