login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240472 Primorial expansion of e. 0
2, 1, 1, 1, 3, 9, 3, 0, 1, 1, 16, 25, 8, 3, 32, 32, 37, 24, 53, 17, 28, 67, 52, 2, 21, 81, 56, 88, 9, 3, 80, 42, 15, 37, 107, 52, 32, 120, 49, 46, 84, 3, 129, 29, 159, 103, 90, 172, 128, 98, 202, 138, 207, 150, 249, 131, 132, 66, 9, 86, 137, 191, 236, 141, 222, 285, 8, 205, 310, 250, 63, 173, 288, 93, 294, 84, 66, 104, 28, 154, 93, 229, 96, 254, 333, 89, 126, 393, 388, 396, 418, 424, 356, 299, 482, 64, 114, 60, 513, 471 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The primorial expansion a(n) of a real number x is defined as x = a(0) + sum(i>0, a(i) / prime(i)# ) where a(0) = floor(x) and 0 <= a(i) < prime(i) for all i > 0.

LINKS

Table of n, a(n) for n=0..99.

FORMULA

x(0) = e;

a(n) = floor(x(n));

x(n + 1) = prime(n) * (x(n) - a(n));

where prime(n) = A000040(n) is the n-th prime number.

a(n) gives the primorial expansion of x(0) = e.

EXAMPLE

e = 2 + 1/prime(1)# + 1/prime(2)# + 1/prime(3)# + 3/prime(4)# + 9/prime(5)# + ...

where prime(n)# = A002110(n) is the n-th primorial.

MATHEMATICA

pe = Block[{x = #, $MaxExtraPrecision = \[Infinity]},

       Do[x = Prime[i] (x - Sow[x // Floor]) // Expand, {i, #2 - 1}];

       x // Floor // Sow] // Reap // Last // Last // Function;

pe[E, 100]

CROSSREFS

Sequence in context: A251660 A279453 A054252 * A007442 A054772 A294616

Adjacent sequences:  A240469 A240470 A240471 * A240473 A240474 A240475

KEYWORD

nonn

AUTHOR

Albert Lau, Apr 06 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 8 01:57 EDT 2020. Contains 336287 sequences. (Running on oeis4.)