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 1-6 of 6 results.

A100787 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

1, 2, 4, 8, 16, 17, 23, 24, 31, 33, 36, 38, 42, 45, 46, 49, 52, 55, 61, 64, 72, 76, 78, 82, 87, 91, 97, 101, 110, 115, 117, 122, 127, 133, 134, 140, 144, 151, 153, 160, 166, 173, 181, 189, 191, 199, 206, 215, 216, 225, 232, 233, 233, 234, 235, 236, 236, 237, 238, 243
Offset: 1

Views

Author

David W. Wilson, Jan 04 2005

Keywords

Examples

			1.2.4.8.16.17.23.24.31 ... <- sequence
.1.2.4.8..1..6..1..7... <- first differences are the sequence's digits.

References

  • E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Links

Crossrefs

First differences are A100880; Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

Programs

  • Maple
    A[1]:= 1: S:= "1":
for n from 2 to 100 do
  A[n]:= A[n-1] + parse(S[n-1]);
  S:= cat(S, A[n]);
od:
seq(A[i], i=1..100); # Robert Israel, Jun 11 2019
  • Mathematica
    a[1] = 1; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jun 15 2005 *)

A107974 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

3, 6, 12, 13, 15, 16, 19, 20, 25, 26, 32, 33, 42, 44, 44, 46, 51, 53, 59, 62, 64, 67, 70, 74, 76, 80, 84, 88, 92, 96, 102, 107, 108, 113, 116, 121, 130, 136, 138, 144, 148, 154, 161, 168, 168, 175, 179, 186, 192, 200, 200, 208, 212, 220, 228, 237, 239, 248, 254, 255
Offset: 1

Views

Author

Eric Angelini, Jun 12 2005

Keywords

Examples

			3.6.12.13.15.16.19.20.25 ... <- sequence
.3.6..1..2..1..3..1..5 ... <- first differences are the sequence's digits.

Crossrefs

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

Programs

  • Mathematica
    a[1] = 3; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jun 15 2005 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 15 2005

A107976 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

7, 14, 15, 19, 20, 25, 26, 35, 37, 37, 39, 44, 46, 52, 55, 60, 63, 70, 73, 80, 83, 92, 96, 100, 104, 110, 115, 117, 122, 127, 133, 133, 139, 142, 149, 149, 156, 159, 167, 167, 175, 178, 187, 189, 198, 204, 205, 205, 205, 206, 206, 210, 211, 212, 212, 213, 214
Offset: 1

Views

Author

Eric Angelini, Jun 12 2005

Keywords

Comments

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

Examples

			7.14.15.19.20.25.26.35.37.37... <- sequence
.7..1..4..1..5..1..9..2..0... <- first differences = the sequence's digits

Programs

  • Mathematica
    a[1] = 7; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jun 15 2005 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 15 2005

A107977 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

9, 18, 19, 27, 28, 37, 39, 46, 48, 56, 59, 66, 69, 78, 82, 88, 92, 100, 105, 111, 116, 125, 131, 137, 143, 152, 159, 167, 175, 177, 185, 193, 202, 204, 205, 205, 205, 206, 206, 211, 212, 213, 214, 215, 216, 222, 223, 225, 230, 231, 234, 235, 236, 239, 246, 247
Offset: 1

Views

Author

Eric Angelini, Jun 12 2005

Keywords

Examples

			9.18.19.27.28.37.39.46.48.56 ... <- sequence
.9..1..8..1..9..2..7..2..8 ... <- first differences are the sequence's digits.

Crossrefs

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

Programs

  • Mathematica
    a[1] = 9; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 56}] (* Robert G. Wilson v, Jun 15 2005 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 15 2005

A240919 Sequence whose n-th term is the sum of the first n digits in the concatenation of the base 10-representation of the sequence.

Original entry on oeis.org

9, 10, 10, 11, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 27, 28, 33, 34, 40, 41, 49, 50, 59, 61, 63, 65, 68, 70, 77, 79, 87, 90, 93, 96, 100, 104, 104, 108, 109, 113, 122, 127, 127, 132, 141, 147, 148, 154, 157, 163
Offset: 1

Views

Author

Anthony Zajac, Aug 02 2014

Keywords

Comments

This is the unique sequence in base 10 with this property, aside from the trivial case of beginning this sequence with a(k)=0 for the first k terms.
The only possible nonzero values for a(1) and a(2) are 9 and 10, respectively. This is because a(1) must be a 1-digit number, while a(2) must equal the sum of its own first digit and a(1).
Likewise, for the analogous sequence in a different base b, the first two terms must be b-1 and b.
Essentially the same as A107975. - R. J. Mathar, Jul 07 2023

Examples

			a(5) is the sum of the first 5 digits of "91010111112..." = 9 + 1 + 0 + 1 + 0 = 11.

Links

Crossrefs

Cf. A004207, A016096, A061939, A065075, A107975.

Programs

  • Mathematica
    a240919 = {};
Do[
Which[Length[a240919] <= 0, AppendTo[a240919, 9],
  Length[a240919] == 1,
  AppendTo[a240919,
   First[First[a240919] +
     IntegerDigits[First[Plus[a240919, a240919]]]]],
  True, AppendTo[a240919,
   Total[Take[Flatten[Map[IntegerDigits, a240919]], n]]]], {n,
  10000}]; TableForm[
Transpose[
  List[Range[Length[a240919]],
   a240919]]] (* Michael De Vlieger, Aug 05 2014 *)
  • PARI
    lista(nn) = {v = vector(nn); v[1] = 9; v[2] = 10; vd = [9, 1, 0]; print1(v[1], ", ", v[2], ", "); for (n=3, nn, v[n] = sum(k=1, n, vd[k]); vd = concat(vd, digits(v[n])); print1(v[n], ", "););} \\ Michel Marcus, Aug 14 2014

A339951 Similar to A100787, but alternate with addition and multiplication instead. See Comments section for more information.

Original entry on oeis.org

1, 2, 4, 8, 64, 70, 280, 287, 0, 2, 16, 16, 32, 40, 280, 280, 560, 561, 3366, 3367, 20202, 20205, 40410, 40414, 0, 2, 16, 16, 32, 40, 0, 5, 30, 30, 150, 156, 156, 159, 477, 483, 2898, 2901, 8703, 8709, 60963, 60965, 0, 2, 0, 2, 4, 4, 8, 8, 40, 44, 0, 4, 4, 4
Offset: 0

Views

Author

Jamie Robert Creasey, Dec 24 2020

Keywords

Comments

We start with a(0) as 1, placing an addition sign below the digit. As such, we add 1 to a(0) to receive the next term which is 2. This time, place a multiplication sign below the new digit and double a(1) to receive a(2) which is 4. Place add under the next unused digit and add this to a(2), followed by multiply under the next a(3) and repeat.
Unlike A100787, terms within this sequence are not strictly increasing, as the 8th digit in this sequence is a 0 where we apply multiplication. Also, the differences do not reflect the digits of this sequence, due to alternation with multiplication. The records are 1, 2, 4, 8, 64, 70, 280, 287, 280, 560, 561, 3366 ...

Examples

			1, 2, 4, 8, 64, 70, 280, 287, 0, 2, 16, ...
+  *  +  *  +*  +*  +*+  *+*  +  *  +*
To calculate a(5), we add 6 to 64, as the 5th digit is a 6 with the add operator underneath. Thus, a(5) is 70.
To calculate a(8), we multiply 287 by 0, as the 8th digit is a 0 with the multiply operator underneath. Thus, a(8) is 0.

Crossrefs

Cf. A100787, A107974, A107975, A107976, A107977.
Showing 1-6 of 6 results.

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