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

3,4

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

Formula

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

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 *)

Prog

(PARI) dsemi(n)= { local(k=0); if(isprime(n), k=0; while(bigomega(n-k)<>2&&k<n, k=k+1)); return(k) }
{ forprime(n=5, 10^3, print(n, " ", dsemi(n))) } \\ Antonio Roldán, Oct 08 2012

Crossrefs

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

Sequence in context: A123359 A376070 A378423 * A187760 A122143 A144868

Adjacent sequences: A121882 A121883 A121884 * A121886 A121887 A121888

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 31 2006

Extensions

Extended by T. D. Noe, Oct 08 2012

Status

approved