A084468 Odd numbers with exactly 3 ones in binary expansion.

7, 11, 13, 19, 21, 25, 35, 37, 41, 49, 67, 69, 73, 81, 97, 131, 133, 137, 145, 161, 193, 259, 261, 265, 273, 289, 321, 385, 515, 517, 521, 529, 545, 577, 641, 769, 1027, 1029, 1033, 1041, 1057, 1089, 1153, 1281, 1537, 2051, 2053, 2057, 2065, 2081, 2113, 2177

Offset: 1

Author

Antti Karttunen, Jun 02 2003

Keywords

• nonn
• base
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.

Crossrefs

Intersection of A005408 and A014311.

A084470(n) gives the position of a(n) in A084467(n).

Cf. A018900.

Programs

Mathematica

Flatten[Table[2^m + 2^n + 1, {m, 2, 11}, {n, m - 1}]] (* Alonso del Arte, Jul 08 2011 *)

PARI

for(m=2, 9, for(n=1, m-1, print1(2^m+2^n+1", "))) \\ Charles R Greathouse IV, Oct 04 2011

Python

from math import isqrt, comb
def A084468(n): return (1<<(m:=isqrt(n<<3)+1>>1)+1)+(1<<(n-comb(m,2)))|1 # Chai Wah Wu, Apr 07 2025

Formula

a(n) = 2*A018900(n) + 1 = A005408(A018900(n)).

Sum_{n>=1} 1/a(n) = 0.714295772926319061998427422200268976390844375453066534198594764887682975019... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022