A028897 If n = Sum c_i 10^i then a(n) = Sum c_i 2^i.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice
• look

Comments

For n<100, this is the same result as "If n = Sum c_i 10^i then a(n) = Sum c_i (i+1)". - Henry Bottomley, Apr 20 2001

n_2 in the notation of A122618.

Left inverse of A007088 (binary numbers), cf. formula from Karttunen. - M. F. Hasler, Jun 13 2023

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Robin C. Yu, Decibinary Numbers, on Hackerrank.com.
• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A007088, A122618.

Differs from A081594 and A244158 for the first time at n = 100, which here is a(100) = 4.

Cf. A249873, A072170.

See A322000 for integers ordered according to the value of a(n).

Programs

Haskell

a028897 0 = 0
a028897 n = 2 * a028897 n' + d where (n', d) = divMod n 10
-- Reinhard Zumkeller, Nov 06 2014

Mathematica

a[n_ /; n < 10] := n; a[n_] := a[n] = If[Mod[n, 10] != 0, a[n-1] + 1, 2*a[n/10]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 02 2016 *)

PARI

a(n)=if(n<1,0,if(n%10,a(n-1)+1,2*a(n/10)))

PARI

A028897(n)=fromdigits(digits(n),2) \\ M. F. Hasler, Feb 14 2019
(MIT/GNU Scheme) (define (A028897 n) (let loop ((z 0) (i 0) (n n)) (if (zero? n) z (loop (+ z (* (modulo n 10) (expt 2 i))) (1+ i) (floor->exact (/ n 10)))))) ;; Antti Karttunen, Jun 22 2014

Formula

a(n) = 2*a(floor(n/10)) + (n mod 10). - Henry Bottomley, Apr 20 2001

a(0) = 0, a(n) = 2*a(n/10) if n == 0 (mod 10), a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 21 2002

For all n, a(A007088(n)) = n. - Antti Karttunen, Jun 22 2014

Extensions

More terms from Erich Friedman.

Terms up to n = 100 added by Antti Karttunen, Jun 22 2014