OFFSET
0,1
COMMENTS
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?
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jul 06 2005
STATUS
approved