A023691 Numbers with exactly 9 ones in binary expansion.

511, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022, 1279, 1407, 1471, 1503, 1519, 1527, 1531, 1533, 1534, 1663, 1727, 1759, 1775, 1783, 1787, 1789, 1790, 1855, 1887, 1903, 1911, 1915, 1917, 1918, 1951, 1967, 1975

Offset

1,1

Links

Ivan Neretin, 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+1) = A057168(a(n)). - M. F. Hasler, Aug 27 2014

Sum_{n>=1} 1/a(n) = 1.386348105265697723853732153017686670695581836109569165990080192653647019078... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Mathematica

Select[ Range[ 511, 2048 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==9)& ]

Prog

(PARI) is_A023691(n)=hammingweight(n)==9 \\ M. F. Hasler, Aug 27 2014
(PARI) print1(t=2^9-1); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 2014
(Python)
from itertools import islice
def A023691_gen(): # generator of terms
    yield (n:=511)
    while True: yield (n:=((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
A023691_list = list(islice(A023691_gen(), 30)) # Chai Wah Wu, Mar 06 2025

Crossrefs

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690 (Hamming weight = 1, 2, ..., 8), A057168.

Sequence in context: A051985 A103206 A277172 * A045118 A043451 A158011

Adjacent sequences: A023688 A023689 A023690 * A023692 A023693 A023694

Keyword

nonn,base,easy,changed

Author

Olivier Gérard

Status

approved