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%I #6 Jun 14 2016 08:45:43
%S 8,6,6,6,4,4,2,2,22,6,8,2,2,20,10,4,6,8,4,4,2,4,20,10,8,6,10,2,2,8,14,
%T 12,20,10,14,20,16,6,14,4,2,8,8,12,2,24,20,10,10,4,48,40,8,34,4,4,38,
%U 56,4,28,2,14,14,22,6,8,10,4,16,4,20,2,26,56,32
%N Difference between first odd semiprime > 3^n and 3^n.
%C A098147 is difference between first odd semiprime > 10^n and 10^n. How can we prove that there exists an a(n) for all n? In this powers of 3 sequence, does 2 occur infinitely often? Does every even integer k > 0 occur?
%F a(n) = minimum integer k such that 3^n + k is an element of A046315. a(n) = minimum integer k such that A000244(n) + k is an element of A046315.
%e a(0) = 8 because 3^0 + 8 = 9 = 3^2 is an odd semiprime.
%e a(1) = 6 because 3^1 + 6 = 9 = 3^2 is an odd semiprime.
%e a(2) = 6 because 3^2 + 6 = 15 = 3 * 5 is an odd semiprime.
%e a(3) = 6 because 3^3 + 6 = 33 = 3 * 11 is an odd semiprime.
%e a(4) = 4 because 3^4 + 4 = 85 = 5 * 17 is an odd semiprime.
%e a(5) = 4 because 3^5 + 4 = 247 = 13 * 19 is an odd semiprime.
%t a[n_] := Block[{z}, z = 3^n + 2; While[ PrimeOmega[z] != 2, z += 2]; z - 3^n]; a /@ Range[0, 60] (* _Giovanni Resta_, Jun 14 2016 *)
%Y Cf. A000244, A001358, A098147.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Feb 03 2006
%E a(26) corrected and more terms from _Giovanni Resta_, Jun 14 2016
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