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

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, 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, 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

Offset: 0

Author

Robert G. Wilson v, Feb 12 2005

Keywords

• base
• nonn

Comments

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

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

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

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

Cf. A000225, A020714.

Programs

Maple

V:= Vector([0]): B:= Vector([0]): m:= 1:
for n from 2 to 200 do
  V(n):= B[n-1] + 2;
  if V[n] >= 10 then
    B(m+1):= 1;
    B(m+2):= V[n] mod 10;
    m:= m+2;
  else
    B(m+1):= V[n];
    m:= m+1;
  fi
od:
convert(V,list); # Robert Israel, Oct 11 2016

Mathematica

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

Formula

From Robert Israel, Oct 11 2016: (Start)

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

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

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))).

(End)