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a(n) = n + number of previous prime terms, a(1) = 1.
1

%I #14 Feb 28 2018 11:30:32

%S 1,2,4,5,7,9,10,11,13,15,16,17,19,21,22,23,25,26,27,28,29,31,33,34,35,

%T 36,37,39,40,41,43,45,46,47,49,50,51,52,53,55,56,57,58,59,61,63,64,65,

%U 66,67,69,70,71,73,75,76,77,78,79,81,82,83,85,86,87,88,89,91,92,93,94

%N a(n) = n + number of previous prime terms, a(1) = 1.

%C Or, a(1)=1; a(n)=a(n-1) + d: if a(n-1) is prime then d=2 otherwise d=1.

%H Vincenzo Librandi, <a href="/A122825/b122825.txt">Table of n, a(n) for n = 1..10000</a>

%t s={1};p=0;Do[b=n+p;AppendTo[s,b];If[PrimeQ[b],p++ ],{n,2,130}];s

%o (PARI) lista(nn) = {print1(a=1, ", "); nbp = 0; for (n=2, nn, newn = nbp + n; print1(newn, ", "); nbp += isprime(newn););} \\ _Michel Marcus_, Jul 31 2017

%Y Cf. A135731 (complement).

%K nonn

%O 1,2

%A _Zak Seidov_, Oct 23 2006