%I #44 Jun 20 2023 17:03:06

%S 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,

%T 7,8,9,10,11,12,13,14,15,8,9,10,11,12,13,14,15,16,17,10,11,12,13,14,

%U 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

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

%C 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

%C n_2 in the notation of A122618.

%C Left inverse of A007088 (binary numbers), cf. formula from Karttunen. - _M. F. Hasler_, Jun 13 2023

%H Reinhard Zumkeller, <a href="/A028897/b028897.txt">Table of n, a(n) for n = 0..10000</a>

%H Robin C. Yu, <a href="https://www.hackerrank.com/challenges/decibinary-numbers">Decibinary Numbers</a>, on Hackerrank.com.

%H <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>

%F a(n) = 2*a(floor(n/10)) + (n mod 10). - _Henry Bottomley_, Apr 20 2001

%F 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

%F For all n, a(A007088(n)) = n. - _Antti Karttunen_, Jun 22 2014

%t 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 *)

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

%o (PARI) A028897(n)=fromdigits(digits(n),2) \\ _M. F. Hasler_, Feb 14 2019

%o (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

%o (Haskell)

%o a028897 0 = 0

%o a028897 n = 2 * a028897 n' + d where (n', d) = divMod n 10

%o -- _Reinhard Zumkeller_, Nov 06 2014

%Y Cf. A007088, A122618.

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

%Y Cf. A249873, A072170.

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

%K nonn,base,easy,nice,look

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_.

%E Terms up to n = 100 added by _Antti Karttunen_, Jun 22 2014