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A291437 Smallest m >= 0 such that (2*n)*3^m + 1 is prime, or -1 if no such value exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A301989 A216513 A364419 * A302231 A228101 A078128
KEYWORD
nonn
AUTHOR
Martin Renner, Aug 23 2017
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)