%I A161896
%S A161896 5,11,23,29,41,53,83,89,113,131,173,179,191,233,239,251,281,293,359,419,
%T A161896 431,443,491,509,593,641,653,659,683,719,743,761,809,911,953,1013,1019,
%U A161896 1031,1049,1103,1223,1229,1289,1409,1439,1451,1481,1499,1511,1541,1559
%N A161896 Integers n for which k = (9^n - 3 * 3^n - 4n) / (2n * (2n + 1)) is an 
               integer
%C A161896 Near superset of the Sophie Germain primes (A005384), excluding 2 and 
               3: 2n + 1 is prime. Nearly all members of this sequence are also 
               prime, but four members less than 10000 are composite:
%C A161896 1541 = 23 * 67
%C A161896 2465 = 5 * 17 * 29
%C A161896 3281 = 17 * 193
%C A161896 4961 = 11^2 * 41
%C A161896 The congruence of n modulo 4 is evenly distributed between 1 and 3. n 
               is congruent to 5 (mod 6) for all n less than two billion.
%C A161896 This sequence has roughly twice the density of the sequence (A158034) 
               corresponding to the Diophantine equation
%C A161896 f = (4^n - 2^n + 8n^2 - 2) / (2n * (2n + 1)),
%C A161896 and contains most members of that sequence. Those it does not contain 
               are composite and often congruent to 3 (mod 6).
%Y A161896 Cf. A161897 A000040, A002515, A005384 A158034, A158035, A158036 A145918
%Y A161896 Sequence in context: A069097 A024921 A152533 this_sequence A167610 A143127 
               A061769
%Y A161896 Adjacent sequences: A161893 A161894 A161895 this_sequence A161897 A161898 
               A161899
%K A161896 easy,nonn
%O A161896 1,1
%A A161896 Reikku Kulon (reikku(AT)gmail.com), Jun 21 2009