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Search: id:A126975
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| A126975 |
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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. |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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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.
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MATHEMATICA
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sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; Prime@Select[Range[240], PrimeQ[sopfr[Prime[ # ] + Prime[ # + 1]]] &] (*Chandler*)
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PROGRAM
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(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 */
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CROSSREFS
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Cf. A086711.
Sequence in context: A038919 A141181 A100031 this_sequence A156314 A023186 A023188
Adjacent sequences: A126972 A126973 A126974 this_sequence A126976 A126977 A126978
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KEYWORD
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nonn,less
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Mar 20 2007
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EXTENSIONS
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Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 25 2007
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