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A276116
Least k such that A001222(k*n) = A001222(k*n+1), or -1 if no such k exists.
1
2, 1, 3, 11, 5, 29, 2, 37, 1, 17, 3, 277, 33, 1, 5, 59, 2, 313, 2, 31, 1, 2, 10, 401, 1, 37, 1, 71, 4, 367, 3, 367, 1, 1, 7, 1259, 8, 1, 11, 83, 4, 347, 2, 1, 3, 5, 2, 6263, 2, 7, 3, 23, 10, 331, 11, 94, 1, 2, 2, 1069, 2, 2, 13, 467, 11, 89, 3, 67, 15, 5, 2, 2467, 8, 4, 1
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
EXAMPLE
a(4) = 11 because A001222(11*4) = A001222(11*4+1).
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
Sequence in context: A340063 A372523 A196371 * A306993 A119928 A215265
KEYWORD
nonn
AUTHOR
Altug Alkan, Aug 19 2016
STATUS
approved