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

Author

Axel Harvey, Jul 24 2006

Keywords

• easy
• nonn
• less

Examples

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

Links

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

Crossrefs

Cf. A000149.

Programs

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 *)

PARI

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

Formula

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

Extensions

More terms from Stefan Steinerberger, Jul 26 2006