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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

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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)