cp's OEIS Frontend

A103694 Add 2 to each of the preceding digits, beginning with 0.

%I A103694 #15 Dec 02 2018 02:46:44
%S A103694 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 A103694 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 A103694 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 A103694 Add 2 to each of the preceding digits, beginning with 0.
%C A103694 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 A103694 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 A103694 Robert Israel, <a href="/A103694/b103694.txt">Table of n, a(n) for n = 0..10000</a>
%F A103694 From _Robert Israel_, Oct 11 2016: (Start)
%F A103694 For 6 <= m <= 10 and k >= 1, a(m*2^k-5) = 2*m-10.
%F A103694 For 5 <= m <= 9, k >= 1 and -4 <= j <= 2^k-6, a(m*2^k+j) = 2*m-7.
%F A103694 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 A103694 (End)
%p A103694 V:= Vector([0]): B:= Vector([0]): m:= 1:
%p A103694 for n from 2 to 200 do
%p A103694   V(n):= B[n-1] + 2;
%p A103694   if V[n] >= 10 then
%p A103694     B(m+1):= 1;
%p A103694     B(m+2):= V[n] mod 10;
%p A103694     m:= m+2;
%p A103694   else
%p A103694     B(m+1):= V[n];
%p A103694     m:= m+1;
%p A103694   fi
%p A103694 od:
%p A103694 convert(V,list); # _Robert Israel_, Oct 11 2016
%t A103694 Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 2]], {0}, 22]]
%Y A103694 Cf. A102654, A103693, A103695, A103696, A103697, A103698, A103699, A103700.
%Y A103694 Cf. A000225, A020714.
%K A103694 base,nonn
%O A103694 0,2
%A A103694 _Robert G. Wilson v_, Feb 12 2005