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

1,3

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

Links

Table of n, a(n) for n=1..34.

Formula

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

a(n) = A000079(n) - A000040(n). - 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}]

Prog

(PARI) vector(50, n, 2^n - prime(n)) \\ Michel Marcus, Sep 23 2014
(Magma) [2^n-NthPrime(n) : n in [1..30]]; // Wesley Ivan Hurt, Sep 23 2014

Crossrefs

Cf. A000040, A000079.

Sequence in context: A369343 A105544 A119917 * A262444 A372559 A109755

Adjacent sequences: A111206 A111207 A111208 * A111210 A111211 A111212

Keyword

nonn,easy

Author

Roger L. Bagula, Oct 25 2005

Extensions

More terms from Michel Marcus, Sep 23 2014

Status

approved