A387961 a(n) is the least k such that k + 2^i has exactly i prime factors, counted with multiplicity, for 1 <= i <= n-1 but not for i = n.

2, 1, 5, 377, 335, 481197, 48032639, 7887570497, 1085946652169

Offset

1,1

Comments

a(n) is odd for n > 1.

Links

Table of n, a(n) for n=1..9.

Formula

A001222(a(n)+2^i) = i for 1 <= i <= n-1 but not for i = n.

Example

a(3) = 5 because 5 + 2 = 7 is prime, 5 + 2^2 = 9 = 3^2 is a semiprime, but 5 + 2^3 = 13 is not a triprime, and none of 1, 2, 3, 4 works.

Maple

g:= proc(x) local i;
     for i from 1 do
       if numtheory:-bigomega(x+2^i) <> i then return i fi
     od
end proc:
V:= Vector(7): count:= 1: V[1]:= 2:
for x from 1 by 2 while count < 7 do
 v:= g(x);
 if V[v] = 0 then V[v]:= x; count:= count+1 fi
od:
convert(V, list);

Prog

(PARI) isok(k, n) = my(v=vector(n, i, k+2^i)); for (i=1, n-1, if (bigomega(v[i]) != i, return(0))); bigomega(v[n]) != n;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Oct 12 2025

Crossrefs

Cf. A001222.

Sequence in context: A323500 A277471 A110863 * A215219 A335931 A091615

Adjacent sequences: A387958 A387959 A387960 * A387962 A387963 A387964

Keyword

nonn,more

Author

Robert Israel, Oct 12 2025

Extensions

a(8)-a(9) from Daniel Suteu, Oct 17 2025

Status

approved