|
%I #5 Sep 08 2022 08:45:24
%S 1,2,3,9,14,20,21,30,36,41,51,68,78,83,95,99,113,131,134,135,138,153,
%T 158,209,216,249,285,299,300,303,315,320,326,350,366,375,378,413,443,
%U 453,455,468,483,488,495,498,510,543,545,615,618,645,699,713,741,771
%N Numbers n such that n+(n+1) is prime and sum of the prime factors of n and n+1 is also prime.
%e 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 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 (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 */
%K nonn
%O 1,2
%A _J. M. Bergot_, Apr 16 2007
%E Edited, corrected and extended by _Klaus Brockhaus_, Apr 17 2007
|
