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Excess of n-th semiprime over previous prime.
1

%I #14 Feb 15 2018 12:57:02

%S 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,

%T 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,

%U 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

%N Excess of n-th semiprime over previous prime.

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

%H Robert G. Wilson v, <a href="/A121884/b121884.txt">Table of n, a(n) for n=1..1000</a>

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

%t 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 *)

%t #-NextPrime[#,-1]&/@Select[Range[400],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Feb 15 2018 *)

%Y Cf. A000040, A001358, A062721, A077068.

%K easy,nonn

%O 1,3

%A _Jonathan Vos Post_, Aug 31 2006

%E a(31)-a(103) from _Robert G. Wilson v_, Mar 16 2009