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A291438
Smallest prime of the form (2*n)*3^m + 1 for some m >= 0, or -1 if no such prime exists.
2
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
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
KEYWORD
nonn
AUTHOR
Martin Renner, Aug 23 2017
STATUS
approved