A109204 - OEIS

%I #10 Jun 18 2016 00:41:37

%S 2,3,5,10,5,2,11,4,7,2,9,4,7,5,3,2,7,16,7,2,39,2,25,12,5,7,21,2,5,3,7,

%T 16,9,17,5,24,19,4,3,20,7,6,11,4,3,4,17,12,17,2,7,70,3,3,5,2,11,16,5,

%U 42,7,4,3,26,3,9,25,26,9,5,33,6,23,12,23,2,9,6,7,2,23,4,3,16,11,16,9,2,3

%N Minimal value of k>0 such that n^9 + k^2 is a semiprime.

%H G. C. Greubel, <a href="/A109204/b109204.txt">Table of n, a(n) for n = 0..1000</a>

%e a(0) = 2 because 0^9 + 1^2 = 1 is not semiprime, but 0^9 + 2^2 = 4 = 2^2 is.

%e a(1) = 3 because 1^9 + 1^2 and 1^9 + 2^2 are not semiprime, but 1^9 + 3^2 = 10 = 2 * 5 is semiprime.

%e a(2) = 5 because 2^9 + 5^2 = 537 = 3 * 179 is semiprime, but 2^9 plus no smaller square is.

%e a(51) = 70 because 51^9 + 70^2 = 2334165173095351 = 43063 * 54203496577 and for no smaller k>0 is 51^9 + k^2 a semiprime.

%e a(100) = 7 because 100^9 + 7^2 = 1000000000000000049 = 157 * 6369426751592357 and for no smaller k>0 is 100^9 + k^2 a semiprime.

%t a[n_] := (For[k = 1, PrimeOmega[n^9 + k^2] != 2, k++]; k); a /@ Range[0, 88] (* _Giovanni Resta_, Jun 17 2016 *)

%o (PARI) a(n) = my(k=1); while(bigomega(n^9+k^2)!=2, k++); k \\ _Felix Fröhlich_, Jun 17 2016

%Y Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Jul 04 2005

%E a(15) corrected by _Giovanni Resta_, Jun 17 2016