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%I #14 May 05 2022 10:07:13
%S 1,2,4,5,7,8,12,14,16,17,19,20,24,26,28,29,35,36,46,48,50,51,53,56,60,
%T 62,66,67,69,70,80,83,85,88,90,91,95,100,102,103,105,106,110,112,116,
%U 117,123,125,129,131,133,134,136,138,144,146,150,151,163,164,170,175
%N a(n) = Sum_{k=1..n} A034693(k).
%H Amiram Eldar, <a href="/A072920/b072920.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) appears to be asymptotic to (zeta(2)-1)*n*log(n) where zeta(2)-1 = Pi^2/6-1 = 0.6449... . Example: a(10^5)/10^5/log(10^5) = 0.6449(1)... .
%t f[n_] := Module[{k = 1}, While[!PrimeQ[k*n + 1], k++]; k]; Accumulate[Table[f[n], {n, 1, 100}]] (* _Amiram Eldar_, May 05 2022 *)
%o (PARI) f(n) = if(n<0, 0, s=1; while(isprime(s*n+1)==0, s++); s); \\ A034693
%o a(n) = sum(k=1, n, f(k)); \\ _Michel Marcus_, May 05 2022
%Y Cf. A013661, A034693.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Aug 11 2002
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