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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A001358 (semiprimes).

Sequence in context: A279794 A025900 A118383 * A108339 A138559 A073454

Adjacent sequences: A115763 A115764 A115765 * A115767 A115768 A115769

Keyword

easy,nonn

Author

T. D. Noe, Jan 30 2006

Status

approved