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Search: id:A104589
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| A104589 |
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a(1)=1. a(n) = a(n-1) + (sum of terms, from among terms a(1) through a(n-1), which are prime or 1). |
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+0
1
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| 1, 2, 5, 13, 34, 55, 76, 97, 215, 333, 451, 569, 1256, 1943, 2630, 3317, 4004, 4691, 10069, 25516, 40963, 56410, 71857, 87304, 102751, 118198, 133645, 149092, 164539, 179986, 195433, 210880, 226327, 241774, 257221, 529889, 802557, 1075225
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By Dirichlet's Theorem there are an infinite number of primes in this sequence.
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EXAMPLE
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The noncomposites among the first 8 terms of the sequence are 1, 2, 5, 13, and 97. The sum of these is 1+2+5+13+97 = 118. So a(9) = a(8) + 118 = 215.
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MATHEMATICA
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f[lst_] := Append[lst, Last(AT) lst + Plus (AT)(AT) Select[lst, (PrimeQ(AT)# || # == 1) &]]; Nest[f, {1}, 38] (* Robert G. Wilson v *).
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CROSSREFS
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Sequence in context: A052988 A001429 A112841 this_sequence A122024 A027931 A103142
Adjacent sequences: A104586 A104587 A104588 this_sequence A104590 A104591 A104592
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Jun 12 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 02 2007
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