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A115766
Distance from the n-th prime to the nearest semiprime.
2
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.
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
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Jan 30 2006
STATUS
approved