A354975 a(n) = Sum_{i=1..n} (prime(i+n) mod prime(i)).

1, 2, 6, 9, 16, 26, 25, 46, 47, 54, 81, 112, 140, 116, 173, 215, 254, 234, 317, 329, 409, 440, 511, 584, 581, 582, 666, 649, 776, 866, 875, 967, 1057, 1152, 1310, 1419, 1246, 1294, 1296, 1551, 1599, 1722, 1970, 2152, 2166, 2154, 2338, 2396, 2523, 2831, 3120, 2867, 3220, 3332, 3274, 3266, 3462

Offset: 1

Author

J. M. Bergot and Robert Israel, Jun 15 2022

Keywords

• nonn

Examples

			For n = 3, a(n) = (7 mod 2) + (11 mod 3) + (13 mod 5) = 1+2+3 = 6.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A207409, A354972, A355009.

Programs

Maple

f:= proc(n) local k;
   add(ithprime(n+k) mod ithprime(k),k=1..n)
end proc:
map(f, [$1..100]);

Mathematica

a[n_]:=Sum[Mod[Prime[i+n],Prime[i]],{i,n}]; Array[a,57] (* Stefano Spezia, Jun 15 2022 *)

PARI

a(n) = sum(i=1, n, prime(i+n) % prime(i)); \\ Michel Marcus, Jun 15 2022

Python

from sympy import prime
def A354975(n): return sum(prime(i+n) % prime(i) for i in range(1,n+1)) # Chai Wah Wu, Jun 19 2022