%I A116222
%S A116222 1,2,3,9,14,20,21,30,36,41,51,68,78,83,95,99,113,131,134,135,138,153,
%T A116222 158,209,216,249,285,299,300,303,315,320,326,350,366,375,378,413,443,
%U A116222 453,455,468,483,488,495,498,510,543,545,615,618,645,699,713,741,771
%N A116222 Numbers n such that n+(n+1) is prime and sum of the prime factors of 
               n and n+1 is also prime.
%e A116222 83+84 = 167 is prime, 83 is prime, 84 = 2^2*3*7. 83+2+2+3+7 = 97 is prime, 
               hence 83 is a term.
%e A116222 95+96 = 191 is prime. 95 = 5*19; 96 = 2^5*3. 5+19+2+2+2+2+2+3 = 37 is 
               prime, hence 95 is a term.
%o A116222 (MAGMA) [1] cat [ n: n in [2..700] | IsPrime(2*n+1) and IsPrime(&+[ &+[ 
               k[1]*k[2]: k in Factorization(h) ]: h in [n,n+1] ] ) ]; /* Klaus 
               Brockhaus, Apr 17 2007 */
%Y A116222 Sequence in context: A048744 A057293 A109662 this_sequence A048038 A113501 
               A101067
%Y A116222 Adjacent sequences: A116219 A116220 A116221 this_sequence A116223 A116224 
               A116225
%K A116222 nonn
%O A116222 1,2
%A A116222 J. M. Bergot (thekingfishb(AT)yahoo.ca), Apr 16 2007
%E A116222 Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Apr 17 2007