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

1,3

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

Formula

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

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 *)

Crossrefs

Cf. A000040, A001358, A062721, A077068.

Sequence in context: A353707 A318438 A294233 * A079087 A324920 A358638

Adjacent sequences: A121881 A121882 A121883 * A121885 A121886 A121887

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 31 2006

Extensions

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

Status

approved