A103694 - OEIS

%I #15 Dec 02 2018 02:46:44

%S 0,2,4,6,8,10,3,2,5,4,7,6,9,8,11,10,3,3,3,2,5,5,5,4,7,7,7,6,9,9,9,8,

%T 11,11,11,10,3,3,3,3,3,3,3,2,5,5,5,5,5,5,5,4,7,7,7,7,7,7,7,6,9,9,9,9,

%U 9,9,9,8,11,11,11,11,11,11,11,10,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,5,5,5,5,5,5

%N Add 2 to each of the preceding digits, beginning with 0.

%C A000225 is hidden here. The sequence shows increasing cycles of the ten digits 1,0,3,2,5,4,7,6,9,8 where the odd digits are repeated while the evens not. The second cycle is 11,10,3,3,3,2,5,5,5,4,7,7,7,6,9,9,9,8 (= three times the same odd digit); the third one shows seven same odd digit... Thus the number of repeating odd digits in the first cycles are: 1, 3, 7, 15, 31, 63, 127, ... which is the sequence A000225. - _Alexandre Wajnberg_, Feb 16 2005

%C A020714 is also hidden here: the total number of digits increasingly repeated of each of the cycles are: 5 (the first five digits), 10, 20, 40, 80, 160, 320, ... which is A020714. - _Alexandre Wajnberg_, Feb 16 2005

%H Robert Israel, <a href="/A103694/b103694.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Robert Israel_, Oct 11 2016: (Start)

%F For 6 <= m <= 10 and k >= 1, a(m*2^k-5) = 2*m-10.

%F For 5 <= m <= 9, k >= 1 and -4 <= j <= 2^k-6, a(m*2^k+j) = 2*m-7.

%F G.f.: (1-x)^(-1)*(2*(x+x^2+x^3+x^4)+3*x^5+Sum_{k>=1} ((-x-7)*x^(5*2^k-5)+Sum_{m=6..9} (-1+3*x)*x^(m*2^k-5))).

%F (End)

%p V:= Vector([0]): B:= Vector([0]): m:= 1:

%p for n from 2 to 200 do

%p   V(n):= B[n-1] + 2;

%p   if V[n] >= 10 then

%p     B(m+1):= 1;

%p     B(m+2):= V[n] mod 10;

%p     m:= m+2;

%p   else

%p     B(m+1):= V[n];

%p     m:= m+1;

%p   fi

%p od:

%p convert(V,list); # _Robert Israel_, Oct 11 2016

%t Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 2]], {0}, 22]]

%Y Cf. A102654, A103693, A103695, A103696, A103697, A103698, A103699, A103700.

%Y Cf. A000225, A020714.

%K base,nonn

%O 0,2

%A _Robert G. Wilson v_, Feb 12 2005