A383030 Indices of the even terms in the sequence of exponentially odd numbers.

2, 5, 7, 8, 11, 16, 18, 19, 22, 24, 26, 29, 31, 33, 35, 39, 41, 43, 46, 48, 51, 54, 56, 58, 61, 63, 67, 69, 72, 74, 76, 79, 82, 84, 86, 87, 91, 93, 96, 98, 100, 103, 106, 109, 110, 113, 115, 119, 121, 122, 124, 126, 129, 131, 133, 136, 139, 144, 147, 149, 152

Offset: 1

Author

Amiram Eldar, Apr 13 2025

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 2/5.

Links

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

Crossrefs

Cf. A268335, A376218, A383029, A383031.

Programs

Mathematica

expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; Position[Select[Range[350], expOddQ], _?EvenQ] // Flatten

PARI

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

Formula

A383029(a(n)) > 0.