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Numbers with exactly 9 ones in binary expansion.
19

%I #18 Feb 14 2022 01:23:51

%S 511,767,895,959,991,1007,1015,1019,1021,1022,1279,1407,1471,1503,

%T 1519,1527,1531,1533,1534,1663,1727,1759,1775,1783,1787,1789,1790,

%U 1855,1887,1903,1911,1915,1917,1918,1951,1967,1975

%N Numbers with exactly 9 ones in binary expansion.

%H Ivan Neretin, <a href="/A023691/b023691.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) = 1.386348105265697723853732153017686670695581836109569165990080192653647019078... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022

%t Select[ Range[ 511, 2048 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==9)& ]

%o (PARI) is_A023691(n)=hammingweight(n)==9 \\ _M. F. Hasler_, Aug 27 2014

%o (PARI) print1(t=2^9-1); for(i=2, 50, print1(", "t=A057168(t))) \\ _M. F. Hasler_, Aug 27 2014

%Y Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690 (Hamming weight = 1, 2, ..., 8), A057168.

%K nonn,base,easy

%O 1,1

%A _Olivier GĂ©rard_