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

Author

Jonathan Vos Post, Sep 01 2006

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000040, A014612, A114403.

Programs

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 *)

Formula

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

A014612(n)}.

Extensions

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