A121884 Excess of n-th semiprime over previous prime.

1, 1, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 4, 1, 2, 3, 2, 4, 2, 4, 5, 1, 4, 2, 1, 4, 3, 2, 3, 4, 2, 4, 5, 6, 3, 2, 2, 5, 6, 8, 9, 10, 2, 2, 3, 2, 3, 4, 6, 7, 4, 1, 2, 4, 3, 2, 4, 5, 2, 4, 6, 1, 2, 3, 4, 6, 7, 10, 2, 3, 4, 6, 7, 8, 10, 3, 2, 4, 6, 8, 2, 3, 2, 5, 2, 4, 3, 1, 4, 6, 8, 2, 5, 6, 8, 9, 10, 12, 2, 1, 2, 4, 6

Offset: 1

Author

Jonathan Vos Post, Aug 31 2006

Keywords

• easy
• nonn

Comments

a(n) = 1 iff n is in A077068. a(n) = 2 iff n is in A062721.

Links

• Robert G. Wilson v, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A000040, A001358, A062721, A077068.

Programs

Mathematica

semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; lst1 = Select[ Range@ 325, semiPrimeQ@# &]; lst = Select[ Range@ 500, semiPrimeQ@# &]; lst - (NextPrime[ #, -1] & /@ lst) (* Robert G. Wilson v, Mar 16 2009 *)
#-NextPrime[#,-1]&/@Select[Range[400],PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 15 2018 *)

Formula

a(n) = Min{A001358(n)-p for p < A001358(n) and p in A000040(k)}.

Extensions

a(31)-a(103) from Robert G. Wilson v, Mar 16 2009