A038461 Sums of 10 distinct powers of 2.

1023, 1535, 1791, 1919, 1983, 2015, 2031, 2039, 2043, 2045, 2046, 2559, 2815, 2943, 3007, 3039, 3055, 3063, 3067, 3069, 3070, 3327, 3455, 3519, 3551, 3567, 3575, 3579, 3581, 3582, 3711, 3775, 3807, 3823, 3831, 3835, 3837, 3838, 3903

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base
• easy

Links

• Ivan Neretin, 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.

Crossrefs

Base 2 interpretation of A038452.

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9).

Programs

Mathematica

Select[Range[4000], DigitCount[#, 2, 1] == 10 &] (* Amiram Eldar, Feb 14 2022 *)

PARI

isok(n) = hammingweight(n) == 10; \\ Michel Marcus, Feb 29 2016

Python

from itertools import islice
def A038461_gen(): # generator of terms
    yield (n:=1023)
    while True: yield (n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
A038461_list = list(islice(A038461_gen(),20)) # Chai Wah Wu, Mar 10 2025

Formula

Sum_{n>=1} 1/a(n) = 1.386312271262110321181505974797071257205562524228381227122302929089588534920... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Extensions

Offset changed to 1 by Ivan Neretin, Feb 28 2016