A254033 Number of primes dividing exactly one number in the next largest gap between primes.

0, 1, 2, 3, 6, 10, 15, 20, 21, 28, 37, 44, 53, 76, 96, 113, 123, 135, 142, 150, 181, 191, 235, 270, 291, 294, 313, 327, 334, 395, 403, 411, 445, 478, 496, 539, 582, 587, 654, 693, 722, 732, 757, 754, 772, 778, 791, 832, 830, 848, 920, 930, 955, 1004, 1053, 1151, 1240

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..75

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A373271 A111467 A215891 * A356314 A102366 A152452

Adjacent sequences: A254030 A254031 A254032 * A254034 A254035 A254036

Keyword

nonn

Author

Mamuka Jibladze, Jan 23 2015

Extensions

a(43)-a(57) from Robert G. Wilson v, Jan 23 2015

Status

approved