A110934 a(n) = A014612(n+2) - A014612(n).

10, 8, 9, 8, 3, 14, 14, 3, 6, 7, 13, 14, 5, 4, 7, 6, 3, 16, 20, 7, 4, 6, 8, 9, 6, 3, 8, 8, 6, 13, 17, 10, 6, 6, 11, 11, 6, 6, 2, 3, 3, 8, 11, 6, 4, 7, 17, 17, 15, 18, 9, 6, 7, 6, 6, 3, 2, 10, 12, 6, 8, 7, 7, 7, 6, 7, 5, 3, 2, 5, 6, 20, 24, 8, 6, 7, 10, 8, 6, 10, 7

Offset

1,1

Comments

Difference between 3-almostprime(n) and 3-almostprime(n+2).

This is the 3-almost prime analog of what A113784 is for semiprimes and what A031131 is for primes. The minimum values in the sequence are 2 because we have, for example, the 3 consecutive 3-almost primes 170, 171, 172, so a(39) = A014612(41) - A014612(39) = 172 - 170 = 2. Equivalently, there are 2 consecutive 1 values of A114403 (3-almost prime gaps; first differences of A014612). This happens for elements of A113789 (numbers n such that n, n+1 and n+2 are 3-almost primes).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A014612(n+2) - A014612(n).

Example

a(1) = 10 because the difference between the first and third 3-almost primes is A014612(3) - A014612(1) = 18 - 8 = 10.
a(2) = A014612(4) - A014612(2) = 20 - 12 = 8.
a(3) = A014612(5) - A014612(3) = 27 - 18 = 9.

Mathematica

#[[3 ;; ]] - #[[;; -3]] & [Select[Range[500], PrimeOmega[#] == 3 &]] (* Paolo Xausa, Oct 06 2025 *)

Crossrefs

Cf. A014612.

Sequence in context: A180197 A280871 A390510 * A291424 A357473 A065691

Adjacent sequences: A110931 A110932 A110933 * A110935 A110936 A110937

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Jan 21 2006

Extensions

a(28) corrected by R. J. Mathar, Dec 22 2010

Status

approved