A116222 - OEIS

%I #12 Aug 20 2024 11:27:03

%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 k such that k+(k+1) is prime and sum of the prime factors of k and k+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.

%t fn[{a_,b_}]:=a*b;Select[Range[771],PrimeQ[#+(#+1)]&&PrimeQ[Total[fn/@FactorInteger[#]]+Total[fn/@FactorInteger[#+1]]]&] (* _James C. McMahon_, Aug 19 2024 *)

%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