A114405 5-almost prime gaps. First differences of A014614.

16, 24, 8, 28, 4, 8, 42, 6, 8, 4, 20, 8, 35, 9, 12, 6, 2, 8, 20, 4, 8, 56, 10, 14, 4, 9, 3, 12, 20, 10, 6, 8, 4, 28, 4, 20, 32, 15, 21, 4, 2, 18, 4, 14, 26, 4, 15, 5, 4, 4, 8, 4, 2, 26, 16, 6, 2, 8, 20, 48, 20, 34, 6, 3, 27, 2, 4, 20, 1, 7, 16, 8, 4, 4, 6, 30, 6, 6, 12, 6, 3, 11

Offset

1,1

Comments

First occurrences of a(n)=1,2,3,.. are at n=69, 17, 27, 5, 48, 8, 70, 3, 14, 23, 82, 15, 150, 24, 38, 1, 172, 42, 258, 11, 39, 135, 102, 2, 779, 45, 65, 4, 518, 76, 263, 37, 211, 62, 13, 1009, 2463, 606, 254, 151, 3348, 7, 4513,... - R. J. Mathar, Oct 06 2007

Links

R. J. Mathar, Table of n, a(n) for n = 1..9999

Formula

a(n) = A014614(n+1) - A014614(n).

Example

a(1) = 16 = 48-32 where 32 is the first 5-almost prime and 48 is the second.
a(2) = 24 = 72-48.
a(3) = 8 = 80-72.
a(4) = 28 = 108-80.
a(5) = 4 = 112-108.
a(6) = 8 = 120-112.
a(7) = 42 = 162-120.
a(8) = 6 = 168-162.
a(13) = 35 = 243-208.
a(22) = 56 = 368-312.

Mathematica

Differences[Select[Range[2000], PrimeOmega[#]==5&]] (* Harvey P. Dale, Sep 28 2019 *)

Crossrefs

Cf. A014614, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

Sequence in context: A225929 A179370 A166675 * A098351 A206267 A325480

Adjacent sequences: A114402 A114403 A114404 * A114406 A114407 A114408

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 25 2005

Extensions

More terms from R. J. Mathar, Oct 06 2007

Status

approved