A262016 a(n) = ( ( Sum_{k=1..n} 2^(prime(k)-1) ) mod n! ) / 2.

0, 0, 2, 7, 15, 83, 91, 5163, 86315, 401323, 14725035, 65973803, 2562459691, 37695987243, 45627576875, 9183900142123, 39579412285995, 2598666482813483, 28017829467228715, 223446104928848427, 275288604322335275, 116723151945719253547, 12606804937123633465899

Offset: 1

Author

R. J. Cano and M. F. Hasler, Sep 08 2015

Keywords

• nonn

Comments

This sequence appears to be dense in semiprimes.

Links

• R. J. Cano, Table of n, a(n) for n = 1..100

Programs

Magma

[(&+[2^(NthPrime(k)-1): k in [1..n]] mod Factorial(n))/2: n in [1..25]]; // Bruno Berselli, Sep 24 2015

Mathematica

Table[Mod[Sum[2^(Prime[k] - 1), {k, n}], n!]/2, {n, 23}] (* Michael De Vlieger, Sep 09 2015 *)

PARI

a(n)=sum(k=1,n,2^(prime(k)-1))%n!/2
for(i=1,30,print1(a(i), ", ")); \\ R. J. Cano, Sep 08 2015