A023689 Numbers with exactly 7 ones in binary expansion.

127, 191, 223, 239, 247, 251, 253, 254, 319, 351, 367, 375, 379, 381, 382, 415, 431, 439, 443, 445, 446, 463, 471, 475, 477, 478, 487, 491, 493, 494, 499, 501, 502, 505, 506, 508, 575, 607, 623, 631, 635, 637, 638, 671, 687

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.

M. I. Mazurkov and A. V. Sokolov, Nonlinear substitution S-boxes based on composite power residue codes, Radioelectronics and Communications Systems, Vol. 56, No. 9 (2013). DOI: 10.3103/S0735272713090045.

Formula

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

Sum_{n>=1} 1/a(n) = 1.386779022721502147026318489565477811900220906277367947393004721391094590038... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Mathematica

Select[ Range[ 127, 704 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==7)& ]

Prog

(PARI) is_A023689(n)=hammingweight(n)==7 \\ M. F. Hasler, Aug 27 2014
(PARI) print1(t=2^7-1); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 2014
(Python)
from itertools import islice
def A023689_gen(): # generator of terms
    yield (n:=127)
    while True: yield (n:=((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
A023689_list =  list(islice(A023689_gen(), 30)) # Chai Wah Wu, Mar 06 2025

Crossrefs

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023690, A023691 (Hamming weight = 1, 2, ..., 9), A057168.

Sequence in context: A137985 A065092 A141916 * A095284 A127579 A107380

Adjacent sequences: A023686 A023687 A023688 * A023690 A023691 A023692

Keyword

nonn,base,easy,changed

Author

Olivier Gérard

Status

approved