A072920 a(n) = Sum_{k=1..n} A034693(k).

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, 62, 66, 67, 69, 70, 80, 83, 85, 88, 90, 91, 95, 100, 102, 103, 105, 106, 110, 112, 116, 117, 123, 125, 129, 131, 133, 134, 136, 138, 144, 146, 150, 151, 163, 164, 170, 175

Offset: 1

Author

Benoit Cloitre, Aug 11 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013661, A034693.

Programs

Mathematica

f[n_] := Module[{k = 1}, While[!PrimeQ[k*n + 1], k++]; k]; Accumulate[Table[f[n], {n, 1, 100}]] (* Amiram Eldar, May 05 2022 *)

PARI

f(n) = if(n<0, 0, s=1; while(isprime(s*n+1)==0, s++); s); \\ A034693
a(n) = sum(k=1, n, f(k)); \\ Michel Marcus, May 05 2022

Formula

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)... .