OFFSET
1,1
COMMENTS
Least k such that k*n is a term of A045920.
Is there n such that a(n) = -1?
From Robert Israel, Sep 25 2024: (Start)
Let b be any number coprime to n with A001222(b) = A001222(n) and b - n odd. Take x and y such that b*x - n*y = 1. Then also b * (x + t*n) - n * (y + t*b) = 1. If there is t such that both x + t*n and y + t*b are prime, then k = y + t*b satisfies A001222(k*n) =A001222(k*n+1) = A001222(n)+1. Dickson's conjecture implies that such t exists.
(End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
MAPLE
f:= proc(n) local k, t, m;
m:= numtheory:-bigomega(n);
for k from 1 do
if m + numtheory:-bigomega(k) = numtheory:-bigomega(k*n+1) then
return k
fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Sep 25 2024
PROG
(PARI) a(n) = {my(k = 1); while(bigomega(k*n) != bigomega(k*n+1), k++); k; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Aug 19 2016
STATUS
approved