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Numbers with exactly 8 ones in binary expansion.
19

%I #17 Feb 14 2022 01:24:00

%S 255,383,447,479,495,503,507,509,510,639,703,735,751,759,763,765,766,

%T 831,863,879,887,891,893,894,927,943,951,955,957,958,975,983,987,989,

%U 990,999,1003,1005,1006,1011,1013,1014,1017

%N Numbers with exactly 8 ones in binary expansion.

%H Ivan Neretin, <a href="/A023690/b023690.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n+1) = A057168(a(n)). - _M. F. Hasler_, Aug 27 2014

%F Sum_{n>=1} 1/a(n) = 1.386455689748809038407077281583569975813437283445124123432573411446506561062... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022

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

%o (PARI) is_A023690(n)=hammingweight(n)==8 \\ _M. F. Hasler_, Aug 27 2014

%o (PARI) print1(t=2^8-1); for(i=2, 50, print1(", "t=A057168(t))) \\ _M. F. Hasler_, Aug 27 2014

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

%K nonn,base,easy

%O 1,1

%A _Olivier GĂ©rard_