A116222 Numbers k such that k+(k+1) is prime and sum of the prime factors of k and k+1 is also prime.

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

Offset

1,2

Links

Table of n, a(n) for n=1..56.

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.

Mathematica

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

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

Sequence in context: A225792 A057293 A109662 * A338234 A048038 A113501

Adjacent sequences: A116219 A116220 A116221 * A116223 A116224 A116225

Keyword

nonn

Author

J. M. Bergot, Apr 16 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 17 2007

Status

approved