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
Keywords
Examples
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.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..1000
Programs
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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 *) -
PARI
a(n) = {my(m = 0); while (!isprime(p=(2*n)*3^m + 1), m++); p;} \\ Michel Marcus, Aug 25 2017
Comments