A109205 -id:A109205 - cp's OEIS frontend

A109206 Minimal value of k>0 such that n^11 + k^2 is a semiprime.

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, 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, 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

Offset: 0

Jonathan Vos Post, Jul 06 2005

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?

			a(0) = 2 because 0^11 + 1^2 = 1 is not semiprime, but 0^11 + 2^2 = 4 = 2^2 is.
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.
a(2) = 1 because 2^11 + 1^2 = 2049 = 3 * 683 is semiprime.
a(35) = 48 because 35^11 + 48^2 = 96549157373049179 = 401 * 240770966017579 and for no smaller k>0 is 35^11 + k^2 a semiprime.
a(100) = 37 because 100^11 + 37^2 = 10000000000000000001369 = 60089 *
166419810614255521 and for no smaller k>0 is 100^11 + k^2 a semiprime.

Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203, A109204, A109205.

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 *)

cp's OEIS Frontend

A109206 Minimal value of k>0 such that n^11 + k^2 is a semiprime.

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