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

1,1

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.

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A005408 and A014311.

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

Cf. A018900.

Sequence in context: A064149 A046289 A092246 * A292315 A372781 A274915

Adjacent sequences: A084465 A084466 A084467 * A084469 A084470 A084471

Keyword

nonn,base,easy

Author

Antti Karttunen, Jun 02 2003

Status

approved