A214490 Smallest integer k such that prime(n+1) = floor(prime(n)/sin(k)).

7, 32, 7, 103, 1, 26, 45, 109, 70, 2, 21, 46, 71, 2, 134, 90, 27, 2, 152, 39, 20, 71, 108, 2, 27, 127, 27, 140, 27, 134, 39, 71, 96, 108, 52, 27, 360, 127, 39, 39, 52, 115, 8, 171, 8, 159, 115, 140, 8, 140, 127, 8, 27, 171, 171, 171, 8, 171, 96, 14, 39, 404

Offset

1,1

Comments

a(n) is given in radians.

It appears that a(n) contains identical values for finite sets of n, for instance :

a(n) = 8 for 22 values of n = 43, 45, 49, 52, 57, 75, 78, 85, 88, 90, 103, 105, 107, 108, 110, 111, 118, 135, 172, 197, 274 and 367;

a(n) = 121 for 107 values of n = 265, 268, 277, 286, …, 3022, 4009;

a(n) = 454 for 148 values of n = 373, 377, 384, 390, …, 4025, 4300.

Links

Michel Lagneau, Table of n, a(n) for n = 1..1000

Example

a(3) = 7 because prime(3+1) = floor(prime(3) / sin(7)) = floor(5/.6569865987...) =  floor(7.610505313…) = 7 = prime(4).

Maple

with(numtheory):for n from 1 to 100 do:i:=0:p0:=ithprime(n):p1:=ithprime(n+1):for k from 1 to 10^7 while(i=0) do:c:=sin(k):if c<>0 and p1=floor(p0/c) then i:=1:printf(`%d, `, k):else fi:od:od:

Crossrefs

Cf. A000040.

Sequence in context: A163083 A101329 A193637 * A360261 A164819 A067811

Adjacent sequences: A214487 A214488 A214489 * A214491 A214492 A214493

Keyword

nonn

Author

Michel Lagneau, Jul 19 2012

Status

approved