cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

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

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

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

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)

A103695 Add 3 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 3, 6, 9, 12, 4, 5, 7, 8, 10, 11, 4, 3, 4, 4, 7, 6, 7, 7, 10, 9, 10, 10, 4, 3, 12, 4, 3, 4, 3, 7, 6, 4, 5, 7, 6, 7, 6, 10, 9, 7, 8, 10, 9, 10, 9, 4, 3, 12, 10, 11, 4, 3, 12, 4, 3, 12, 7, 6, 4, 5, 4, 3, 4, 4, 7, 6, 4, 5, 7, 6, 4, 5, 10, 9, 7, 8, 7, 6, 7, 7, 10, 9, 7, 8, 10, 9, 7, 8, 4, 3, 12, 10, 11, 10
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Links

Crossrefs

Cf. A102654, A103693, A103694, A103696, A103697, A103698, A103699, A103700.

Programs

  • Maple
    A[0]:= 0: Agenda:= [0];
for n from 1 to 100 do
  t:= Agenda[1] + 3;
  if t <= 9 then Agenda:= [op(Agenda[2..-1]),t]
  else Agenda:= [op(Agenda[2..-1]),1,t-10]
  fi;
  A[n]:= t;
od:
seq(A[i],i=0..100); # Robert Israel, Dec 14 2017
  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 3]], {0}, 17]]

A102654 Add 7 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 7, 14, 8, 11, 15, 8, 8, 8, 12, 15, 15, 15, 8, 9, 8, 12, 8, 12, 8, 12, 15, 16, 15, 8, 9, 15, 8, 9, 15, 8, 9, 8, 12, 8, 13, 8, 12, 15, 16, 8, 12, 15, 16, 8, 12, 15, 16, 15, 8, 9, 15, 8, 10, 15, 8, 9, 8, 12, 8, 13, 15, 8, 9, 8, 12, 8, 13, 15, 8, 9, 8, 12, 8, 13, 8, 12, 15, 16, 8, 12, 15, 8, 7
Offset: 0

Views

Author

Alexandre Wajnberg, Feb 02 2005

Keywords

Examples

			Add 7 to the first "7" gives 14
Add 7 to the "1" of this 14 gives 8; and adding 7 to the "4" of this 14 gives 11.

Crossrefs

Cf. A103693, A103694, A103695, A103696, A103697, A103698, A103699, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 7]], {0}, 10]] (* Robert G. Wilson v, Feb 04 2005 *)

Extensions

More terms from Robert G. Wilson v, Feb 04 2005

A103696 Add 4 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 4, 8, 12, 5, 6, 9, 10, 13, 5, 4, 5, 7, 9, 8, 9, 11, 13, 12, 13, 5, 5, 5, 7, 5, 6, 5, 7, 9, 9, 9, 11, 9, 10, 9, 11, 13, 13, 13, 5, 5, 13, 5, 4, 13, 5, 5, 5, 7, 5, 7, 5, 7, 9, 9, 5, 7, 9, 8, 5, 7, 9, 9, 9, 11, 9, 11, 9, 11, 13, 13, 9, 11, 13, 12, 9, 11, 13, 13, 13, 5, 5, 13, 5, 5, 13, 5, 5, 5, 7
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Crossrefs

Cf. A102654, A103693, A103694, A103695, A103697, A103698, A103699, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 4]], {0}, 14]]

A103697 Add 5 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 5, 10, 6, 5, 11, 10, 6, 6, 6, 5, 11, 11, 11, 10, 6, 6, 6, 6, 6, 6, 6, 5, 11, 11, 11, 11, 11, 11, 11, 10, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Crossrefs

Cf. A102654, A103693, A103694, A103695, A103696, A103698, A103699, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 5]], {0}, 11]]

A103698 Add 6 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 6, 12, 7, 8, 13, 14, 7, 9, 7, 10, 13, 15, 13, 7, 6, 7, 9, 7, 11, 7, 9, 13, 12, 13, 15, 13, 7, 7, 13, 15, 7, 9, 7, 8, 7, 9, 7, 11, 7, 9, 13, 13, 7, 9, 7, 11, 13, 15, 13, 14, 13, 15, 13, 7, 7, 13, 15, 7, 9, 7, 9, 13, 15, 13, 7, 7, 7, 9, 7, 11, 7, 9, 7, 10, 7, 9, 7, 11, 7, 9, 13, 13, 7, 9, 7, 11
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Crossrefs

Cf. A102654, A103693, A103694, A103695, A103696, A103697, A103699, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 6]], {0}, 11]]

A103699 Add 8 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 8, 16, 9, 14, 17, 9, 12, 9, 15, 17, 9, 10, 17, 9, 13, 9, 15, 17, 9, 8, 9, 15, 17, 9, 11, 17, 9, 13, 9, 15, 17, 16, 17, 9, 13, 9, 15, 17, 9, 9, 9, 15, 17, 9, 11, 17, 9, 13, 9, 15, 9, 14, 9, 15, 17, 9, 11, 17, 9, 13, 9, 15, 17, 17, 17, 9, 13, 9, 15, 17, 9, 9, 9, 15, 17, 9, 11, 17, 9, 13, 17
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Crossrefs

Cf. A102654, A103693, A103694, A103695, A103696, A103697, A103698, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 8]], {0}, 9]]

A103693 Add 1 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 2, 1, 10, 3, 2, 2, 1, 4, 3, 3, 2, 5, 4, 4, 3, 6, 5, 5, 4, 7, 6, 6, 5, 8, 7, 7, 6, 9, 8, 8, 7, 10, 9, 9, 8, 2, 1, 10, 10, 9, 3, 2, 2, 1, 2, 1, 10, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 6, 5, 5, 4, 5, 4, 4, 3, 7, 6, 6
Offset: 0

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Crossrefs

Cf. A102654, A103694, A103695, A103696, A103697, A103698, A103699, A103700.

Programs

  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 1]], {0}, 34]]

A103708 a(n+1) = d(n)+9 where d(n) is the n-th decimal digit in the concatenation of the digits in the sequence, starting with a(1)=1.

Original entry on oeis.org

1, 10, 10, 9, 10, 9, 18, 10, 9, 18, 10, 17, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9, 10, 14, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10
Offset: 1

Views

Author

Robert G. Wilson v, Feb 12 2005

Keywords

Links

Crossrefs

Cf. A103700, A103701, A103702, A103703, A103704, A103705, A103706, A103707.

Programs

  • Maple
    with(queue):
Q:= new(1): R:= 1:
for iter from 1 to 100 do
  v:= dequeue(Q)+9;
  R:= R, v;
  L:= convert(v,base,10);
  for i from 1 to nops(L) do enqueue(Q,L[-i]) od;
od:
R; # Robert Israel, Jul 06 2020
  • Mathematica
    Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 9]], {1}, 8]]

Extensions

Edited and corrected by Robert Israel, Jul 06 2020

A369603 S is a "boomerang sequence": adding 9 to each digit of S and following the result with a comma leaves S unchanged.

Original entry on oeis.org

10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9, 10, 14, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9, 10, 13, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9
Offset: 1

Views

Author

Eric Angelini and Giorgos Kalogeropoulos, Jan 27 2024

Keywords

Comments

Lexicographically earliest sequence starting with a(1) = 10.
The only integers that appear in the sequence are 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18.
Is this (apart from the first term) the same as A103700? - R. J. Mathar, Feb 12 2024

Examples

			Adding 9 to 1 (the 1st digit of 10) gives 10
Adding 9 to 0 (the 2nd digit of 10) gives 9
Adding 9 to 9 (the only digit of 9) gives 18
Adding 9 to 1 (the 1st digit of 18) gives 10
Adding 9 to 8 (the 2nd digit of 18) gives 17, etc.
We see that the last column above is the sequence S itself.

Links

Crossrefs

Cf. A103700, A369604, A369798, A369823, A369824.

Programs

  • Mathematica
    a[1]=10;a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a,n-1]][[n]]+9;Array[a,100]
  • Python
    from itertools import islice
def agen(): # generator of terms
    an, digits = 10, [0]
    while True:
        yield an
        an = 9 + digits.pop(0)
        digits += list(map(int, str(an)))
print(list(islice(agen(), 84))) # Michael S. Branicky, Jan 27 2024
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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