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A121906
Excess of n-th 3-almost prime A014612 over previous prime.
1
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.
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
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Sep 01 2006
EXTENSIONS
a(13) corrected by R. J. Mathar, Dec 22 2010
STATUS
approved