A099249 Number of numbers not greater than n such that length in binary representation and number of ones are coprime.

1, 2, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2004

Keywords

• nonn
• base

Comments

Number of numbers m <= n such that A099244(m) = 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000120, A007088, A063524, A070939, A099244, A099247.

Programs

Haskell

a099249 n = a099249_list !! (n-1)
a099249_list = scanl1 (+) $ map ((0 ^) . (subtract 1)) a099244_list
-- Reinhard Zumkeller, Oct 10 2013

Mathematica

Accumulate[Table[Boole[CoprimeQ[BitLength[n], DigitCount[n, 2, 1]]], {n, 1, 100}]] (* Amiram Eldar, Jul 16 2023 *)

PARI

isA099247(k) = {my(b = binary(k)); gcd(#b, vecsum(b)) == 1;}
list(nmax) = {my(c = 0); for(n = 1, nmax, if(isA099247(n), c++); print1(c, ", "));} \\ Amiram Eldar, Jul 26 2025

Formula

a(n) = Sum_{k=1..n} A063524(A099244(k)). - Reinhard Zumkeller, Oct 10 2013