A121906 Excess of n-th 3-almost prime A014612 over previous prime.

1, 1, 1, 1, 4, 5, 1, 1, 1, 2, 3, 5, 2, 5, 1, 3, 2, 3, 5, 3, 1, 2, 1, 2, 1, 1, 3, 4, 11, 12, 3, 1, 8, 9, 2, 3, 1, 2, 3, 4, 5, 1, 2, 1, 5, 7, 9, 2, 8, 1, 11, 1, 2, 3, 5, 1, 3, 4, 5, 4, 1, 4, 3, 5, 2, 4, 2, 1, 1, 2, 3, 7, 9, 3, 3, 1, 5, 8, 1, 2

Offset

1,5

Comments

a(n) = 1 iff n-th 3-almost prime is of form prime + 1 (not yet in OEIS). See also: A109067 3-almost primes of the form semiprime + 1.

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = Min{A014612(n) - p where p is in A000040 and 1<p < A014612(n)}.

Example

a(1) = 8 - 7 = 1; a(2) = 12 - 11 = 1; a(3) = 18 - 17 = 1;
a(4) = 20 - 19 = 1; a(5) = 27 - 23 = 4; a(6) = 28 - 23 = 5;
a(7) = 30 - 29 = 1.

Maple

A014612 := proc(n) option remember; local a; if n = 1 then 8; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 3 then return a; end if; end do: end if; end proc:
A121906 := proc(n) local t; t := A014612(n) ; t-prevprime(t) ; end proc:
seq(A121906(n), n=1..80) ; # R. J. Mathar, Dec 22 2010

Mathematica

lim=335; p3=Select[Range[lim], PrimeOmega[#] == 3 &] ; l3=Length[p3]; Table[p3[[n]]-NextPrime[p3[[n]], -1], {n, l3}] (* James C. McMahon, Oct 24 2024 *)

Crossrefs

Cf. A000040, A014612, A114403.

Sequence in context: A211799 A113950 A269944 * A028360 A010301 A335862

Adjacent sequences: A121903 A121904 A121905 * A121907 A121908 A121909

Keyword

nonn

Author

Jonathan Vos Post, Sep 01 2006

Extensions

a(13) corrected by R. J. Mathar, Dec 22 2010

Status

approved