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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

(list; graph; refs; listen; history; text; internal format)

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)& ]

Union[FromDigits[#, 2]&/@Permutations[{1, 1, 1, 1, 1, 1, 1, 0, 0, 0}]] (* Harvey P. Dale, Dec 27 2025 *)

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