cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A023690 Numbers with exactly 8 ones in binary expansion.

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%I A023690 #21 Mar 06 2025 14:52:40
%S A023690 255,383,447,479,495,503,507,509,510,639,703,735,751,759,763,765,766,
%T A023690 831,863,879,887,891,893,894,927,943,951,955,957,958,975,983,987,989,
%U A023690 990,999,1003,1005,1006,1011,1013,1014,1017
%N A023690 Numbers with exactly 8 ones in binary expansion.
%H A023690 Ivan Neretin, <a href="/A023690/b023690.txt">Table of n, a(n) for n = 1..10000</a>
%H A023690 Robert Baillie, <a href="http://arxiv.org/abs/0806.4410">Summing the curious series of Kempner and Irwin</a>, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.
%F A023690 a(n+1) = A057168(a(n)). - _M. F. Hasler_, Aug 27 2014
%F A023690 Sum_{n>=1} 1/a(n) = 1.386455689748809038407077281583569975813437283445124123432573411446506561062... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022
%t A023690 Select[ Range[ 255, 1024 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==8)& ]
%o A023690 (PARI) is_A023690(n)=hammingweight(n)==8 \\ _M. F. Hasler_, Aug 27 2014
%o A023690 (PARI) print1(t=2^8-1); for(i=2, 50, print1(", "t=A057168(t))) \\ _M. F. Hasler_, Aug 27 2014
%o A023690 (Python)
%o A023690 from itertools import count, islice
%o A023690 def A023690_gen(): # generator of terms
%o A023690     n = 255
%o A023690     while True:
%o A023690         yield n
%o A023690         n = ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b
%o A023690 A023690_list = list(islice(A023690_gen(),30)) # _Chai Wah Wu_, Mar 06 2025
%Y A023690 Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023691 (Hamming weight = 1, 2, ..., 9), A057168.
%K A023690 nonn,base,easy
%O A023690 1,1
%A A023690 _Olivier Gérard_