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.
%I A014313 #35 Mar 07 2025 01:11:52
%S A014313 31,47,55,59,61,62,79,87,91,93,94,103,107,109,110,115,117,118,121,122,
%T A014313 124,143,151,155,157,158,167,171,173,174,179,181,182,185,186,188,199,
%U A014313 203,205,206,211,213,214,217,218,220,227,229,230,233,234,236,241,242
%N A014313 Numbers with exactly 5 ones in binary expansion.
%C A014313 Appears to give all n such that 4096 is the highest power of 2 dividing A005148(n). - _Benoit Cloitre_, Jun 22 2002
%H A014313 T. D. Noe, <a href="/A014313/b014313.txt">Table of n, a(n) for n = 1..10000</a>
%H A014313 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 A014313 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A014313 a(n+1) = A057168(a(n)). - _M. F. Hasler_, Aug 27 2014
%F A014313 A038447(n) = A007088(a(n)). - _Reinhard Zumkeller_, Jan 06 2015
%F A014313 Sum_{n>=1} 1/a(n) = 1.390704528210321982529622080740025763242354253694629591331835888395977392151... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022
%t A014313 Select[ Range[31, 240], Total[IntegerDigits[#, 2]] == 5&]
%o A014313 (PARI) sum_of_bits(n) = if(n<1, 0, sum_of_bits(floor(n/2))+n%2)
%o A014313 isA014313(n) = (sum_of_bits(n) == 5); \\ _Michael B. Porter_, Oct 21 2009
%o A014313 (PARI) is(n)=hammingweight(n)==5 \\ _Charles R Greathouse IV_, Nov 17 2013
%o A014313 (PARI) print1(t=2^5-1); for(i=2, 50, print1(", "t=A057168(t))) \\ _M. F. Hasler_, Aug 27 2014
%o A014313 (Haskell)
%o A014313 a014313 = f . a038447 where
%o A014313 f x = if x == 0 then 0 else 2 * f x' + b where (x', b) = divMod x 10
%o A014313 -- _Reinhard Zumkeller_, Jan 06 2015
%o A014313 (Python)
%o A014313 from itertools import islice
%o A014313 def A014313_gen(): # generator of terms
%o A014313 yield (n:=31)
%o A014313 while True: yield (n:=((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
%o A014313 A014313_list = list(islice(A014313_gen(),30)) # _Chai Wah Wu_, Mar 06 2025
%Y A014313 Cf. A000079, A018900, A014311, A014312, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9).
%Y A014313 Cf. A005148, A007088, A038447, A057168.
%K A014313 nonn,base,easy
%O A014313 1,1
%A A014313 Al Black (gblack(AT)nol.net)
%E A014313 Extension and program by _Olivier Gérard_