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%I #6 Aug 06 2012 20:28:46
%S 2,3,1,2,3,6,1,4,9,8,13,4,1,2,3,8,7,6,5,28,3,4,5,6,5,2,9,4,9,6,29,2,
%T 15,7,5,48,5,5,33,8,7,24,17,4,15,14,11,4,5,8,9,10,7,6,31,8,3,4,5,18,
%U 13,34,5,2,5,18,35,12,15,2,27,6,31,5,3,34,5,9,7,2,3,4,13,14,23,2,15,22,21,48
%N Minimal value of k>0 such that n^11 + k^2 is a semiprime.
%C It seems that one or more primes almost always occur before finding the first such semiprime for a given n. There seems to be a modest correlation with the n^10 sequence (A109205) with often the same values [n = 0,1,15,21,22,24,31,36,58,81,94]. Or differs by 10 [n = 10,12,60,65,67, 86, 92,100]. Or 20 [n = 41, 46] or 30 [n = 38, 54,75]. Sometimes A109206(n) = A109205(n) = A109204(n) [n = 58,81]. Is it obvious that there must be a k for each n and not an infinite sequence of nonsemiprimes of the form n^11 + k^2?
%e a(0) = 2 because 0^11 + 1^2 = 1 is not semiprime, but 0^11 + 2^2 = 4 = 2^2 is.
%e a(1) = 3 because 1^11 + 1^2 and 1^11 + 2^2 are not semiprime, but 1^11 + 3^2 = 10 = 2 * 5 is semiprime.
%e a(2) = 1 because 2^11 + 1^2 = 2049 = 3 * 683 is semiprime.
%e a(35) = 48 because 35^11 + 48^2 = 96549157373049179 = 401 * 240770966017579 and for no smaller k>0 is 35^11 + k^2 a semiprime.
%e a(100) = 37 because 100^11 + 37^2 = 10000000000000000001369 = 60089 *
%e 166419810614255521 and for no smaller k>0 is 100^11 + k^2 a semiprime.
%t mk[n_]:=Module[{n11=n^11,k=1},While[PrimeOmega[n11+k^2]!=2,k++];k]; Array[ mk,100,0] (* _Harvey P. Dale_, Aug 06 2012 *)
%Y Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203, A109204, A109205.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Jul 06 2005
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