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 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. 0

%I

%S 2,5,23,43,83,97,103,131,149,157,179,191,193,229,251,293,337,383,397,

%T 401,431,443,463,541,569,601,643,709,739,857,859,863,887,907,911,967,

%U 971,983,1019,1039,1069,1091,1093,1223,1229,1249,1279,1283,1321,1373

%N 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.

%e 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.

%t sopfr[n_] := Plus @@ Times @@@ FactorInteger[n];Prime@Select[Range, PrimeQ[sopfr[Prime[ # ] + Prime[ # + 1]]] &] (* _Ray Chandler_, Mar 25 2007 *)

%o (MAGMA) [ p: p in PrimesUpTo(1400) | IsPrime(&+[ k*k: k in Factorization(p+NextPrime(p)) ] ) ]; /* Klaus Brockhaus, Mar 25 2007 */

%o (PARI) {m=1400; p=2; while(p<m, q=nextprime(p+1); f=factor(p+q); if(isprime(sum(j=1, matsize(f), f[j, 1]*f[j, 2])), print1(p, ",")); p=q)} /* Klaus Brockhaus, Mar 25 2007 */

%Y Cf. A086711.

%K nonn,less

%O 1,1

%A _J. M. Bergot_, Mar 20 2007

%E Corrected and extended by _Ray Chandler_ and _Klaus Brockhaus_, Mar 25 2007

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Last modified August 11 08:50 EDT 2020. Contains 336422 sequences. (Running on oeis4.)