

A116222


Numbers n such that n+(n+1) is prime and sum of the prime factors of n and n+1 is also prime.


0



1, 2, 3, 9, 14, 20, 21, 30, 36, 41, 51, 68, 78, 83, 95, 99, 113, 131, 134, 135, 138, 153, 158, 209, 216, 249, 285, 299, 300, 303, 315, 320, 326, 350, 366, 375, 378, 413, 443, 453, 455, 468, 483, 488, 495, 498, 510, 543, 545, 615, 618, 645, 699, 713, 741, 771
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OFFSET

1,2


LINKS



EXAMPLE

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.
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.


PROG

(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 */


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



