A115766 - OEIS

%I #8 May 04 2019 16:06:47

%S 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,

%T 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,

%U 1,3,2,1,2,2,2,1,2,1,2,2,2,1,4,4,2,2,2

%N Distance from the n-th prime to the nearest semiprime.

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

%H T. D. Noe, <a href="/A115766/b115766.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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}]]

%t 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 *)

%Y Cf. A001358 (semiprimes).

%K easy,nonn

%O 1,1

%A _T. D. Noe_, Jan 30 2006