A023690 Numbers with exactly 8 ones in binary expansion.

255, 383, 447, 479, 495, 503, 507, 509, 510, 639, 703, 735, 751, 759, 763, 765, 766, 831, 863, 879, 887, 891, 893, 894, 927, 943, 951, 955, 957, 958, 975, 983, 987, 989, 990, 999, 1003, 1005, 1006, 1011, 1013, 1014, 1017

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) = 1.386455689748809038407077281583569975813437283445124123432573411446506561062... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Mathematica

Select[ Range[ 255, 1024 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==8)& ]

Prog

(PARI) is_A023690(n)=hammingweight(n)==8 \\ M. F. Hasler, Aug 27 2014
(PARI) print1(t=2^8-1); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 2014
(Python)
from itertools import count, islice
def A023690_gen(): # generator of terms
    n = 255
    while True:
        yield n
        n = ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b
A023690_list = list(islice(A023690_gen(), 30)) # Chai Wah Wu, Mar 06 2025

Crossrefs

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023691 (Hamming weight = 1, 2, ..., 9), A057168.

Sequence in context: A257021 A359445 A306223 * A101745 A182221 A053339

Adjacent sequences: A023687 A023688 A023689 * A023691 A023692 A023693

Keyword

nonn,base,easy,changed

Author

Olivier Gérard

Status

approved