A115766 Distance from the n-th prime to the nearest semiprime.

2, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 2, 3, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 5, 3, 1, 2, 2, 2, 2, 3, 2, 3, 4, 1, 2, 1, 4, 1, 2, 3, 1, 3, 2, 2, 2, 1, 3, 2, 2, 4, 2, 2, 1, 2, 3, 1, 3, 4, 2, 2, 2, 1, 2, 2, 2, 1, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 4, 4, 2, 2, 2

Offset: 1

Author

T. D. Noe, Jan 30 2006

Keywords

• easy
• nonn

Comments

This is a very slow-growing function. For the first 10^8 primes, the largest value is 45, which occurs for the prime 981270947.

Examples

			a(10)=3 because 29 is the 10th prime and the nearest semiprime is 26.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes).

Programs

Mathematica

SemiPrimeQ[n_] := (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Join[{2}, Table[p=Prime[i]; j=1; While[ !SemiPrimeQ[p+j] && !SemiPrimeQ[p-j], j++ ]; j, {i, 2, 150}]]
dnsm[n_]:=Module[{k=1},While[PrimeOmega[n-k]!=2&&PrimeOmega[n+k]!=2,k++];k]; dnsm/@Prime[Range[90]] (* Harvey P. Dale, May 04 2019 *)