A111209 Difference between the powers of two and the primes.

0, 1, 3, 9, 21, 51, 111, 237, 489, 995, 2017, 4059, 8151, 16341, 32721, 65483, 131013, 262083, 524221, 1048505, 2097079, 4194225, 8388525, 16777127, 33554335, 67108763, 134217625, 268435349, 536870803, 1073741711, 2147483521, 4294967165, 8589934455, 17179869045

Offset: 1

Author

Roger L. Bagula, Oct 25 2005

Keywords

• nonn
• easy

Comments

2*a(n) < a(n+1) because 2*prime(n) > prime(n+1) (see A062234). We have a(n) - a(1) < a(n+1) - a(n) so this is a B_2 sequence. - Thomas Ordowski, Sep 23 2014

Crossrefs

Cf. A000040, A000079.

Programs

Magma

[2^n-NthPrime(n) : n in [1..30]]; // Wesley Ivan Hurt, Sep 23 2014

Maple

A111209:=n->2^n-ithprime(n): seq(A111209(n), n=1..30); # Wesley Ivan Hurt, Sep 23 2014

Mathematica

Table[2^n - Prime[n], {n, 25}]

PARI

vector(50, n, 2^n - prime(n)) \\ Michel Marcus, Sep 23 2014

Formula

a(n) = 2^n - prime(n).

a(n) = A000079(n) - A000040(n). - Wesley Ivan Hurt, Sep 23 2014

Extensions

More terms from Michel Marcus, Sep 23 2014