A217612 Difference between n-th prime and the smallest semiprime greater than it.

2, 1, 1, 2, 3, 1, 4, 2, 2, 4, 2, 1, 5, 3, 2, 2, 3, 1, 2, 3, 1, 3, 2, 2, 9, 5, 3, 4, 2, 2, 2, 2, 4, 2, 6, 4, 1, 3, 2, 4, 4, 2, 3, 1, 4, 2, 2, 3, 8, 6, 2, 8, 6, 2, 2, 2, 5, 3, 1, 6, 4, 2, 2, 3, 1, 2, 3, 2, 8, 6, 2, 2, 4, 4, 2, 3, 2, 1, 2, 2, 3, 1, 6, 4, 6, 2, 2

Offset

1,1

Comments

Similar to A121885, but with smallest semiprime greater than it.

Links

Antonio Roldán, Table of n, a(n) for n = 1..1229

Formula

a(n) = A102414(n) - A000040(n).

Example

a(7) = 4, because 17 is the seventh prime and 17+1 = 18 = 2*3^2, 17+2 = 19 = 19 and 17+3 = 20 = 2^2*5 are not semiprimes, but 17+4 = 21 = 3*7 is a semiprime.

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++]; i - Prime[n], {n, 87}] (* T. D. Noe, Oct 08 2012 *)
ssp[p_]:=Module[{k=1}, While[PrimeOmega[p+k]!=2, k++]; k]; Table[ssp[p], {p, Prime[ Range[100]]}] (* Harvey P. Dale, Sep 15 2022 *)

Prog

(PARI) m=0; forprime(n=2, 10000, k=0; while(bigomega(n+k)<>2, k=k+1); m=m+1; write("B217612.txt", m, "  ", k)) \\ Antonio Roldán, Oct 08 2012

Crossrefs

Sequence in context: A288158 A319522 A366344 * A029254 A063740 A072782

Adjacent sequences: A217609 A217610 A217611 * A217613 A217614 A217615

Keyword

nonn

Author

Antonio Roldán, Oct 08 2012

Status

approved