A119380 Remainder when the integer part of e^n is divided by the n-th prime number.

0, 1, 0, 5, 5, 0, 8, 16, 7, 15, 13, 28, 23, 23, 26, 24, 57, 57, 62, 43, 70, 49, 36, 64, 84, 3, 4, 64, 83, 103, 45, 53, 49, 37, 26, 19, 75, 20, 147, 20, 134, 73, 56, 17, 31, 89, 143, 200, 103, 170, 25, 37, 159, 181, 90, 242, 16, 93, 222, 163, 57, 132, 214, 71, 164, 57, 62, 14

Offset

1,4

Links

Iain Fox, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor(e^n) mod prime(n).

Example

The sixth term is 0 because e^6 is 403.42879... and 403 is a multiple of 13, the sixth prime.

Maple

A119380:=n->floor(exp(1)^n) mod ithprime(n): seq(A119380(n), n=1..100); # Wesley Ivan Hurt, Nov 30 2017

Mathematica

Table[Mod[Floor[E^n], Prime[n]], {n, 1, 100}] (* Stefan Steinerberger, Jul 26 2006 *)

Prog

(PARI) a(n) = floor(exp(n))%prime(n) \\ Iain Fox, Nov 30 2017

Crossrefs

Cf. A000149.

Sequence in context: A200516 A233383 A144184 * A121212 A182787 A133337

Adjacent sequences: A119377 A119378 A119379 * A119381 A119382 A119383

Keyword

easy,nonn,less

Author

Axel Harvey, Jul 24 2006

Extensions

More terms from Stefan Steinerberger, Jul 26 2006

Status

approved