A114313 - OEIS

%I #7 Sep 05 2013 00:04:26

%S 8,4,0,4,4,2,2,2,4,4,2,2,4,14,4,2,18,6,2,12,16,2,4,2,42,6,4,2,22,26,

%T 12,18,18,38,12,14,2,6,36,2,16,24,6,14,12,6,28,24,24,8,16,32,16,28,12,

%U 8,16,6,16,98

%N Difference between first odd semiprime >= 5^n and 5^n.

%C A098147 is difference between first odd semiprime > 10^n and 10^n.

%F a(n) = minimum integer k such that 5^n + k is an element of A046315. a(n) = minimum integer k such that A000351(n) + k is an element of A046315.

%e a(0) = 8 because 5^0 + 8 = 9 = 3^2 is an odd semiprime; note that because 5^0 + 3 = 4 = 2^2 is an even semiprime, but we only care about odd semiprimes here.

%e a(1) = 4 because 5^1 + 4 = 9 = 3^2 is an odd semiprime.

%e a(2) = 0 because 5^2 + 0 = 25 = 5^2 is an odd semiprime; there are no more zero values.

%e a(3) = 4 because 5^3 + 4 = 129 = 3 * 43.

%e a(4) = 4 because 5^4 + 4 = 629 = 17 * 37.

%e a(5) = 2 because 5^5 + 2 = 3127 = 53 * 59.

%e a(6) = 2 because 5^6 + 2 = 15627 = 3 * 5209.

%e a(7) = 2 because 5^7 + 2 = 78127 = 7 * 11161.

%e a(8) = 4 because 5^8 + 4 = 390629 = 577 * 677 (brilliant).

%e a(9) = 4 because 5^9 + 4 = 1953129 = 3 * 651043.

%t dfpsn[n_]:=Module[{n5=5^n,s},s=If[OddQ[n5],n5,n5+1];While[PrimeOmega[s] != 2,s=s+2];s-n5]; Array[dfpsn,60,0] (* _Harvey P. Dale_, Sep 04 2013 *)

%Y Cf. A000351, A001358, A098147.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Feb 05 2006

%E Corrected and extended by _Harvey P. Dale_, Sep 04 2013