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Search: id:A127269
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| A127269 |
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Suppose the sum of the prime factors of the composites between prime(n) and prime(n+1) is prime. Sequence gives prime(n). |
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| 5, 7, 11, 67, 97, 103, 107, 109, 113, 163, 173, 197, 263, 283, 331, 359, 389, 409, 419, 431, 461, 463, 521, 569, 599, 607, 659, 761, 787, 797, 809, 811, 829, 857, 877, 911, 1019, 1039, 1061, 1087, 1093, 1277, 1283, 1289, 1301, 1409, 1427, 1451, 1481, 1627
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OFFSET
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1,1
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EXAMPLE
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Prime(4) = 7, prime(5) = 11. Sum of prime factors of 8 is 2+2+2 = 6, sum of prime factors of 9 is 3+3 = 6, sum of prime factors of 10 is 2+5= 7; 6+6+7 = 19 is prime, hence prime(4) = 7 is a term.
Prime(19) = 67, prime(20) = 71. Sum of prime factors of 68, 69, 70 is resp. 2+2+17 = 21, 3+23 = 26, 2+5+7 = 14; 21+26+14 = 61 is prime, hence prime(19) = 67 is a term.
Prime(26) = 101, prime(27) = 103. Sum of prime factors of 102 = 2*3*17 is 22, which is composite. Hence prime(26) = 101 is not in the sequence.
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PROGRAM
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(MAGMA) [ p: p in [ NthPrime(k): k in [2..258] ] | IsPrime(&+[ &+[ k[1]*k[2]: k in Factorization(c) ]: c in [p+1..NextPrime(p)-1] ] ) ]; /* Klaus Brockhaus, Mar 29 2007 */
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CROSSREFS
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Sequence in context: A045968 A066367 A098036 this_sequence A071781 A091509 A027728
Adjacent sequences: A127266 A127267 A127268 this_sequence A127270 A127271 A127272
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Mar 27 2007
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EXTENSIONS
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Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 29 2007
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