A092754 a(1)=1, a(2n)=2a(n)+1, a(2n+1)=2a(n)+2.

1, 3, 4, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 22, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 127, 128, 129, 130, 131, 132

Offset: 1

Author

Benoit Cloitre, Apr 13 2004

Keywords

• easy
• nonn

Comments

More generally the sequence b(1)=1, b(2n)=2b(n)+x, b(2n+1)=2b(n)+y is given by the formula b(n)=A053644(n)+x*(n-A053644(n))+y*(A053644(n)-1).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053644 (x=y=0), A054429(x=-1, y=+1), A062050(x=+1, y=-1).

Cf. A206332 (complement).

Cf. A004754.

Programs

Haskell

a092754 n = if n < 2 then n else 2 * a092754 n' + m + 1
            where (n',m) = divMod n 2
a092754_list = map a092754 [1..]
-- Reinhard Zumkeller, May 07 2012

PARI

a(n)=if(n<2,1,if(n%2,a(n-1)+1,a(n/2)*2+1))

PARI

a(n) = n + 1<Kevin Ryde, Jun 19 2021

Formula

a(n) = 2^floor(log(n)/log(2)) + n - 1.

a(n) = A004754(n) - 1. - Rémy Sigrist, May 05 2019