%I A114187
%S A114187 3,3,7,0,1,1,1,1,1,5,1,3,17,1,1,7,7,3,23,1,1,11,29,3,1,1,1,37,1,41,47,
%T A114187 19,11,11,1,7,3,41,1,13,127,47,59,17,37,61,37,59,1,61,73,59,79,73,1,1,
%U A114187 61,149,37,1,1
%N A114187 Difference between first semiprime > n! and n!. Least k such that n!+k 
               is semiprime.
%C A114187 a(n) = 1 when n!+1 is a factorial prime. A098147 is difference between 
               first odd semiprime > 10^n and 10^n. In this sequence, does 1 occur 
               infinitely often (next with n = 71, 75)? If not 0 (for n=3) or 1, 
               a(n) = k must be a prime other than 5. Does every odd prime but 5 
               occur? Some of these take longer to factor, when both prime factors 
               are large, such as n = 37, 38, 42, 47, 50, 54.
%F A114187 a(n) = minimum integer k such that n! + k is an element of A001358. a(n) 
               = minimum integer k such that A000142(n) + k is an element of A001358.
%e A114187 a(0) = a(1) = 3 because 0! + 3 = 1! + 3 = 4 = 2^2 is semiprime (the only 
               even example).
%e A114187 a(2) = 7 because 2! + 7 = 2 + 7 = 9 = 3^2 is semiprime.
%e A114187 a(3) = 0 because 3! + 0 = 6 = 2*3 is semiprime (6+3=9=3^2 so this term 
               would be 3 if we required nonzero values).
%e A114187 a(4) = 1 because 4! + 1 = 24 + 1 = 25 = 5^2 is semiprime.
%e A114187 a(5) = 1 because 5! + 1 = 120 + 1 = 121 = 11^2 is semiprime.
%e A114187 a(6) = 1 because 6! + 1 = 720 + 1 = 721 = 7 * 103 is semiprime.
%e A114187 a(7) = 1 because 7! + 1 = 5040 + 1 = 5041 = 71^2 is semiprime.
%e A114187 a(8) = 1 because 8! + 1 = 40320 + 1 = 40321 = 61 * 661 is semiprime.
%e A114187 a(9) = 5 because 9! + 5 = 362880 + 1 = 362885 = 5 * 72577 is semiprime.
%e A114187 a(10) = 1 because 10! + 1 = 3628800 + 1 = 3628801 = 11 * 329891 is semiprime.
%e A114187 638111
%Y A114187 Cf. A000142, A001358, A098147.
%Y A114187 Sequence in context: A019235 A103895 A066358 this_sequence A118031 A059527 
               A101457
%Y A114187 Adjacent sequences: A114184 A114185 A114186 this_sequence A114188 A114189 
               A114190
%K A114187 easy,nonn
%O A114187 0,1
%A A114187 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 04 2006