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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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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| 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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MATHEMATICA
| spfQ[n_]:=Module[{strt=First[n]+1, end=Last[n]-1}, PrimeQ[Total[Times@@@ Flatten[ FactorInteger[ Range[ strt, end]], 1]]]]; Transpose[Select[ Partition[ Prime[ Range[300]], 2, 1], spfQ]][[1]] (* From Harvey P. Dale, May 06 2011 *)
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PROG
| (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
| Sequence in context: A045968 A066367 A098036 * A071781 A091509 A027728
Adjacent sequences: A127266 A127267 A127268 * A127270 A127271 A127272
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KEYWORD
| nonn
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AUTHOR
| J. M. Bergot (thekingfishb(AT)yahoo.ca), Mar 27 2007
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EXTENSIONS
| Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 29 2007
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