

A217612


Difference between nth prime and the smallest semiprime greater than it.


1



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
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OFFSET

1,1


COMMENTS

Similar to A121885, but with smallest semiprime greater than it.


LINKS

Antonio Roldán, Table of n, a(n) for n = 1..1229


FORMULA

a(n) = A102414(n)  A000040(n).


EXAMPLE

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.


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 *)


PROG

(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


CROSSREFS

Sequence in context: A133771 A288158 A319522 * A029254 A063740 A072782
Adjacent sequences: A217609 A217610 A217611 * A217613 A217614 A217615


KEYWORD

nonn


AUTHOR

Antonio Roldán, Oct 08 2012


STATUS

approved



