A126975 Primes p with property that, if q is the next prime, then the sum of the prime factors of p+q, taken with multiplicity, is a prime.

2, 5, 23, 43, 83, 97, 103, 131, 149, 157, 179, 191, 193, 229, 251, 293, 337, 383, 397, 401, 431, 443, 463, 541, 569, 601, 643, 709, 739, 857, 859, 863, 887, 907, 911, 967, 971, 983, 1019, 1039, 1069, 1091, 1093, 1223, 1229, 1249, 1279, 1283, 1321, 1373

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

97 is a member: 97 + 101 = 198. Its factors with multiplicity are 2*3*3*11 and their sum is 2+3+3+11=19, which is a prime.

Mathematica

sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; Prime@Select[Range[240], PrimeQ[sopfr[Prime[ # ] + Prime[ # + 1]]] &] (* Ray Chandler, Mar 25 2007 *)

Prog

(Magma) [ p: p in PrimesUpTo(1400) | IsPrime(&+[ k[1]*k[2]: k in Factorization(p+NextPrime(p)) ] ) ]; /* Klaus Brockhaus, Mar 25 2007 */
(PARI) {m=1400; p=2; while(p<m, q=nextprime(p+1); f=factor(p+q); if(isprime(sum(j=1, matsize(f)[1], f[j, 1]*f[j, 2])), print1(p, ", ")); p=q)} /* Klaus Brockhaus, Mar 25 2007 */

Crossrefs

Cf. A086711.

Sequence in context: A100031 A293213 A215278 * A175444 A233443 A156314

Adjacent sequences: A126972 A126973 A126974 * A126976 A126977 A126978

Keyword

nonn,less

Author

J. M. Bergot, Mar 20 2007

Extensions

Corrected and extended by Ray Chandler and Klaus Brockhaus, Mar 25 2007

Status

approved