A291437 Smallest m >= 0 such that (2*n)*3^m + 1 is prime, or -1 if no such value exists.

0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 4, 0, 0, 2, 0, 2, 1, 0, 1, 9, 0, 0, 4, 1, 0, 2, 0, 0, 1, 1, 0, 1, 0, 2, 4, 0, 1, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 3, 1, 2, 4, 1, 1, 0, 2, 0, 1, 5, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 80, 0, 6, 0, 8, 2, 0, 1

Offset

1,4

Comments

There exist even integers 2*n such that (2*n)*3^m + 1 is always composite.

It is conjectured that the smallest one is 125050976086 = A123159(3), therefore a(62525488043) = -1.

For the corresponding primes see A291438.

a(A005097(n)) = 0 and a(A047845(n+1)) > 0 (or = -1).

Links

Table of n, a(n) for n=1..87.

Example

a(4) = 2 because this is the smallest value such that 8*3^2 + 1 = 73 is prime, since 8*3^0 + 1 = 9 and 8*3^1 + 1 = 25 are not prime.

Maple

a:=[]:
for n from 1 to 10^3 do
  t:=-1:
  for m from 0 to 10^3 do # this max value of m is sufficient up to n=10^3
    if isprime((2*n)*3^m+1) then t:=m: break: fi:
  od:
  a:=[op(a), t]:
od:
a;

Mathematica

Table[SelectFirst[Range[0, 10^3], PrimeQ[2 n*3^# + 1] &] /. k_ /; MissingQ@ k -> -1, {n, 104}] (* Michael De Vlieger, Aug 23 2017 *)

Prog

(PARI) a(n) = {my(m = 0); while (!isprime(p=(2*n)*3^m + 1), m++); m; } \\ Michel Marcus, Aug 25 2017

Crossrefs

Cf. A005097, A046067, A047845, A123159, A291438.

Sequence in context: A301989 A216513 A364419 * A302231 A228101 A078128

Adjacent sequences: A291434 A291435 A291436 * A291438 A291439 A291440

Keyword

nonn

Author

Martin Renner, Aug 23 2017

Status

approved