A068425 a(n) = floor(2^n*Pi).

1, 3, 6, 12, 25, 50, 100, 201, 402, 804, 1608, 3216, 6433, 12867, 25735, 51471, 102943, 205887, 411774, 823549, 1647099, 3294198, 6588397, 13176794, 26353589, 52707178, 105414357, 210828714, 421657428, 843314856, 1686629713

Offset

-1,2

Comments

In other words, take the binary expansion of Pi, drop the decimal point and interpret the first n+2 bits as an integer.

Dubickas proves that infinitely many terms of this sequence are divisible by 2 or 3 (and hence infinitely many composites). - Charles R Greathouse IV, Feb 04 2016

Links

G. C. Greubel, Table of n, a(n) for n = -1..3300

Artūras Dubickas, Prime and composite integers close to powers of a number, Monatsh. Math. 158:3 (2009), pp. 271-284.

Example

The binary expansion of Pi (A004601) begins 1, 1. 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, ... so we get 1, 3, 6, 12, 25, 50, ...

Mathematica

Table[Floor[2^n*Pi], {n, -1, 100}] (* G. C. Greubel, Mar 23 2018 *)

Prog

(PARI) a(n)=floor(Pi<<n) \\ Charles R Greathouse IV, Feb 04 2016
(Magma) R:= RealField(); [Floor(2^n*Pi(R)): n in [-1..100]]; // G. C. Greubel, Mar 23 2018

Crossrefs

Cf. A004601, A117721 (primes).

Sequence in context: A278666 A007239 A088970 * A329355 A136444 A077854

Adjacent sequences: A068422 A068423 A068424 * A068426 A068427 A068428

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 09 2002

Extensions

Revised by N. J. A. Sloane (and offset changed), Jul 23 2006

Status

approved