A361228 a(n) is the first number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n; a(0) = 0.

0, 2, 4, 66, 1012, 14630, 929390, 63798350

Offset

0,2

Comments

a(8) > 3*10^9 if it exists.

Links

Table of n, a(n) for n=0..7.

Formula

A001222(a(i) + a(j)) = j for 0 <= i < j.

Example

a(3) = 66 because a(0) + 66 = 66 = 2*3*11, a(1) + 66 = 68 = 2*2*17, and a(2) + 66 = 70 = 2*5*7 all have 3 prime factors, counted with multiplicity, and 66 is the least number that works.

Maple

A:= [0]:
for i from 1 to 7 do
 for x from 2^i do if andmap(t -> numtheory:-bigomega(t+x) = i, A) then
    A:= [op(A), x]; break
fi od od:
A;

Crossrefs

Cf. A001222.

Sequence in context: A118993 A219735 A279969 * A018364 A100603 A362456

Adjacent sequences: A361225 A361226 A361227 * A361229 A361230 A361231

Keyword

nonn,more

Author

Robert Israel, Mar 21 2023

Status

approved