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A104589 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). 1
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

By Dirichlet's Theorem there are an infinite number of primes in this sequence.

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

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.

MATHEMATICA

f[lst_] := Append[lst, Last@ lst + Plus @@ Select[lst, (PrimeQ@ # || # == 1) &]]; Nest[f, {1}, 38] (* Robert G. Wilson v, Jul 02 2007 *)

CROSSREFS

Sequence in context: A271940 A273721 A112841 * A154101 A122024 A252932

Adjacent sequences:  A104586 A104587 A104588 * A104590 A104591 A104592

KEYWORD

nonn

AUTHOR

Leroy Quet, Jun 12 2007

EXTENSIONS

More terms from Robert G. Wilson v, Jul 02 2007

STATUS

approved

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Last modified June 18 20:04 EDT 2021. Contains 345121 sequences. (Running on oeis4.)