A383029 Exponent of the highest power of 2 dividing the n-th exponentially odd number.

0, 1, 0, 0, 1, 0, 3, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 1, 0, 0, 1, 0, 5, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 5, 0, 0, 1, 0, 3, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 3, 1

Offset: 1

Author

Amiram Eldar, Apr 13 2025

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A268335, A383030.

Programs

Mathematica

expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; IntegerExponent[Select[Range[200], expOddQ], 2]

PARI

isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if(!(f[i, 2] % 2), return (0))); 1; }
list(lim) = for(k = 1, lim, if(isexpodd(k), print1(valuation(k, 2), ", ")));

Formula

a(n) = A007814(A268335(n)).

a(A383030(n)) > 0.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2/3.