A121885 Excess of n-th prime over previous semiprime.

1, 1, 1, 3, 2, 4, 1, 3, 5, 2, 2, 4, 1, 2, 1, 3, 2, 2, 4, 2, 1, 2, 2, 6, 8, 1, 3, 2, 4, 2, 3, 5, 3, 5, 2, 2, 1, 4, 1, 3, 4, 6, 3, 5, 2, 2, 1, 3, 7, 2, 4, 2, 3, 1, 2, 4, 3, 3, 5, 2, 2, 2, 4, 3, 2, 2, 1, 3, 7, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 4, 4, 6, 2, 6, 2, 3, 3

Offset: 3

Author

Jonathan Vos Post, Aug 31 2006

Keywords

• easy
• nonn
• changed

Comments

See: A102415 Greatest semiprime less than n-th prime. See: A102414 Smallest semiprime greater than n-th prime.

Links

• T. D. Noe, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000040, A001358, A062721, A077068, A102414, A102415.

Programs

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Table[i = Prime[n] - 1; While[! SemiPrimeQ[i], i--]; Prime[n] - i, {n, 3, 100}] (* T. D. Noe, Oct 08 2012 *)
eps[n_]:=Module[{c=n-1},While[PrimeOmega[c]!=2,c--];n-c]; Table[eps[n],{n,Prime[Range[3,90]]}] (* Harvey P. Dale, Aug 12 2014 *)

PARI

dsemi(n)= { local(k=0); if(isprime(n),k=0;while(bigomega(n-k)<>2&&kAntonio Roldán, Oct 08 2012

Formula

a(n) = Min{A000040(n)-s for s < A000040(n) and s in A001358(k)}. a(n) = A000040(n) - A102415(n).

Extensions

Extended by T. D. Noe, Oct 08 2012