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

0,2

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

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)

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]]

Crossrefs

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

Cf. A000225, A020714.

Sequence in context: A114973 A004522 A004521 * A357379 A083167 A338741

Adjacent sequences: A103691 A103692 A103693 * A103695 A103696 A103697

Keyword

base,nonn

Author

Robert G. Wilson v, Feb 12 2005

Status

approved