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A073883
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a(1)=1. For n > 1, a(n) = the smallest positive integer not included earlier such that the n-th partial sum is n times a prime.
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3
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1, 3, 2, 6, 13, 5, 19, 7, 43, 11, 33, 61, 17, 45, 79, 23, 125, 29, 67, 31, 157, 37, 129, 41, 91, 147, 47, 215, 53, 233, 59, 123, 259, 203, 71, 143, 73, 301, 235, 83, 329, 89, 433, 97, 277, 101, 195, 103, 299, 107, 209, 109, 321, 113, 883, 127, 355, 131, 485, 137
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OFFSET
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1,2
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COMMENTS
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Equivalently, for n > 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of the first n terms is prime. - Derek Orr, Jun 26 2015
Conjectured not to be a permutation of the natural numbers. The numbers that have not been used before the 2000th term: 4, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, ... - Derek Orr, Jun 26 2015
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LINKS
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PROG
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(PARI) v=[1]; n=1; while(#v<200, s=(n+vecsum(v))/(#v+1); if(type(s)=="t_INT", if(isprime(s)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0)); n++); v \\ Derek Orr, Jun 26 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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