A291438 Smallest prime of the form (2*n)*3^m + 1 for some m >= 0, or -1 if no such prime exists.

3, 5, 7, 73, 11, 13, 43, 17, 19, 61, 23, 73, 79, 29, 31, 97, 103, 37, 3079, 41, 43, 397, 47, 433, 151, 53, 163, 1102249, 59, 61, 5023, 193, 67, 613, 71, 73, 223, 229, 79, 241, 83, 757, 6967, 89, 271, 277, 283, 97, 883, 101, 103, 313, 107, 109, 331, 113, 3079

Offset

1,1

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 numbers m see A291437.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Example

a(4) = 73 because 8*3^2 + 1 = 73 is the smallest prime of this form, 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), (2*n)*3^t+1]:
od:
a;

Mathematica

Table[If[# < 0, #, 1 + 2 n*3^#] &@ SelectFirst[Range[0, 10^3], PrimeQ[2 n*3^# + 1] &] /. k_ /; MissingQ@ k -> -1, {n, 60}] (* Michael De Vlieger, Aug 23 2017 *)

Prog

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

Crossrefs

Cf. A057025, A123159, A291437.

Sequence in context: A065913 A137999 A353141 * A056145 A119939 A306573

Adjacent sequences: A291435 A291436 A291437 * A291439 A291440 A291441

Keyword

nonn

Author

Martin Renner, Aug 23 2017

Status

approved