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
Keywords
Examples
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.
Links
- Antonio Roldán, Table of n, a(n) for n = 1..1229
Programs
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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 *) -
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
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