A014313 Numbers with exactly 5 ones in binary expansion.

31, 47, 55, 59, 61, 62, 79, 87, 91, 93, 94, 103, 107, 109, 110, 115, 117, 118, 121, 122, 124, 143, 151, 155, 157, 158, 167, 171, 173, 174, 179, 181, 182, 185, 186, 188, 199, 203, 205, 206, 211, 213, 214, 217, 218, 220, 227, 229, 230, 233, 234, 236, 241, 242

Offset

1,1

Comments

Appears to give all n such that 4096 is the highest power of 2 dividing A005148(n). - Benoit Cloitre, Jun 22 2002

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.

Index entries for 2-automatic sequences.

Formula

a(n+1) = A057168(a(n)). - M. F. Hasler, Aug 27 2014

A038447(n) = A007088(a(n)). - Reinhard Zumkeller, Jan 06 2015

Sum_{n>=1} 1/a(n) = 1.390704528210321982529622080740025763242354253694629591331835888395977392151... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Mathematica

Select[ Range[31, 240], Total[IntegerDigits[#, 2]] == 5&]

Prog

(PARI) sum_of_bits(n) = if(n<1, 0, sum_of_bits(floor(n/2))+n%2)
isA014313(n) = (sum_of_bits(n) == 5); \\ Michael B. Porter, Oct 21 2009
(PARI) is(n)=hammingweight(n)==5 \\ Charles R Greathouse IV, Nov 17 2013
(PARI) print1(t=2^5-1); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 2014
(Haskell)
a014313 = f . a038447 where
   f x = if x == 0 then 0 else 2 * f x' + b  where (x', b) = divMod x 10
-- Reinhard Zumkeller, Jan 06 2015
(Python)
from itertools import islice
def A014313_gen(): # generator of terms
    yield (n:=31)
    while True: yield (n:=((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
A014313_list = list(islice(A014313_gen(), 30)) # Chai Wah Wu, Mar 06 2025

Crossrefs

Cf. A000079, A018900, A014311, A014312, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9).

Cf. A005148, A007088, A038447, A057168.

Sequence in context: A033661 A219243 A046047 * A095318 A130096 A229624

Adjacent sequences: A014310 A014311 A014312 * A014314 A014315 A014316

Keyword

nonn,base,easy,changed

Author

Al Black (gblack(AT)nol.net)

Extensions

Extension and program by Olivier Gérard

Status

approved