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%I #31 Feb 14 2022 01:24:17
%S 31,47,55,59,61,62,79,87,91,93,94,103,107,109,110,115,117,118,121,122,
%T 124,143,151,155,157,158,167,171,173,174,179,181,182,185,186,188,199,
%U 203,205,206,211,213,214,217,218,220,227,229,230,233,234,236,241,242
%N Numbers with exactly 5 ones in binary expansion.
%C Appears to give all n such that 4096 is the highest power of 2 dividing A005148(n). - _Benoit Cloitre_, Jun 22 2002
%H T. D. Noe, <a href="/A014313/b014313.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.
%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F a(n+1) = A057168(a(n)). - _M. F. Hasler_, Aug 27 2014
%F A038447(n) = A007088(a(n)). - _Reinhard Zumkeller_, Jan 06 2015
%F Sum_{n>=1} 1/a(n) = 1.390704528210321982529622080740025763242354253694629591331835888395977392151... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022
%t Select[ Range[31, 240], Total[IntegerDigits[#, 2]] == 5&]
%o (PARI) sum_of_bits(n) = if(n<1, 0, sum_of_bits(floor(n/2))+n%2)
%o isA014313(n) = (sum_of_bits(n) == 5); \\ _Michael B. Porter_, Oct 21 2009
%o (PARI) is(n)=hammingweight(n)==5 \\ _Charles R Greathouse IV_, Nov 17 2013
%o (PARI) print1(t=2^5-1); for(i=2, 50, print1(", "t=A057168(t))) \\ _M. F. Hasler_, Aug 27 2014
%o (Haskell)
%o a014313 = f . a038447 where
%o f x = if x == 0 then 0 else 2 * f x' + b where (x', b) = divMod x 10
%o -- _Reinhard Zumkeller_, Jan 06 2015
%Y Cf. A000079, A018900, A014311, A014312, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9).
%Y Cf. A005148, A007088, A038447, A057168.
%K nonn,base,easy
%O 1,1
%A Al Black (gblack(AT)nol.net)
%E Extension and program by _Olivier Gérard_
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