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%I #28 Jul 22 2022 19:40:32
%S 1,2,5,13,34,55,76,97,215,333,451,569,1256,1943,2630,3317,4004,4691,
%T 10069,25516,40963,56410,71857,87304,102751,118198,133645,149092,
%U 164539,179986,195433,210880,226327,241774,257221,529889,802557,1075225
%N 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).
%C By Dirichlet's Theorem there are an infinite number of primes in this sequence.
%H Michel Marcus, <a href="/A104589/b104589.txt">Table of n, a(n) for n = 1..2000</a>
%F a(n) = 3*a(n-1) - a(n-2) if a(n-1) is prime, else a(n) = 2*a(n-1) - a(n-2) for n>3. - _John Tyler Rascoe_, Jul 20 2022
%e 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.
%t f[lst_] := Append[lst, Last@ lst + Plus @@ Select[lst, (PrimeQ@ # || # == 1) &]]; Nest[f, {1}, 38] (* _Robert G. Wilson v_, Jul 02 2007 *)
%o (PARI) lista(nn) = my(va = vector(nn), s = 1); va[1] = 1; for (n=2, nn, va[n] = va[n-1] + s; if (isprime(va[n]), s += va[n]);); va; \\ _Michel Marcus_, Jul 21 2022
%Y Cf. A008578.
%K nonn
%O 1,2
%A _Leroy Quet_, Jun 12 2007
%E More terms from _Robert G. Wilson v_, Jul 02 2007
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