|
|
A309120
|
|
a(n) is the least k > 1 such that n*k is adjacent to a prime.
|
|
2
|
|
|
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 3, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6, 3, 6, 5, 2, 2, 2, 2, 4, 2, 2, 2, 4, 5, 4, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 6, 2, 2, 3, 2, 2, 2, 3, 4, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If n is odd then a(n) is even.
a(n) exists by Dirichlet's theorem on primes in arithmetic progressions.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(13)=4 because 4*13+1=53 is prime but none of 2*13-1,2*13+1,3*13-1,3*13+1 are primes.
|
|
MAPLE
|
f:= proc(m) local k;
for k from 2 by 1+(m mod 2) do
if isprime(k*m-1) or isprime(k*m+1) then return k fi
od
end proc:
map(f, [$1..100]);
|
|
MATHEMATICA
|
a[n_]:=Module[{k=2}, While[Not[PrimeQ[k*n-1]||PrimeQ[k*n+1]], k++]; k];
|
|
PROG
|
(PARI) a(n) = my(k=2); while (!isprime(n*k+1) && !isprime(n*k-1), k++); k; \\ Michel Marcus, Jul 19 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|