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%I #10 Sep 08 2022 08:45:29
%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[240], PrimeQ[sopfr[Prime[ # ] + Prime[ # + 1]]] &] (* _Ray Chandler_, Mar 25 2007 *)
%o (Magma) [ p: p in PrimesUpTo(1400) | IsPrime(&+[ k[1]*k[2]: 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)[1], 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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