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A114313 Difference between first odd semiprime >= 5^n and 5^n.

%I A114313 #7 Sep 05 2013 00:04:26
%S A114313 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 A114313 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 A114313 8,16,6,16,98
%N A114313 Difference between first odd semiprime >= 5^n and 5^n.
%C A114313 A098147 is difference between first odd semiprime > 10^n and 10^n.
%F A114313 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 A114313 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 A114313 a(1) = 4 because 5^1 + 4 = 9 = 3^2 is an odd semiprime.
%e A114313 a(2) = 0 because 5^2 + 0 = 25 = 5^2 is an odd semiprime; there are no more zero values.
%e A114313 a(3) = 4 because 5^3 + 4 = 129 = 3 * 43.
%e A114313 a(4) = 4 because 5^4 + 4 = 629 = 17 * 37.
%e A114313 a(5) = 2 because 5^5 + 2 = 3127 = 53 * 59.
%e A114313 a(6) = 2 because 5^6 + 2 = 15627 = 3 * 5209.
%e A114313 a(7) = 2 because 5^7 + 2 = 78127 = 7 * 11161.
%e A114313 a(8) = 4 because 5^8 + 4 = 390629 = 577 * 677 (brilliant).
%e A114313 a(9) = 4 because 5^9 + 4 = 1953129 = 3 * 651043.
%t A114313 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 A114313 Cf. A000351, A001358, A098147.
%K A114313 easy,nonn
%O A114313 0,1
%A A114313 _Jonathan Vos Post_, Feb 05 2006
%E A114313 Corrected and extended by _Harvey P. Dale_, Sep 04 2013