A068425 - OEIS

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

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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).