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 1-4 of 4 results.

A267806 a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 2) + a(n-2).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 3, 3, 4, 3, 5, 4, 5, 5, 6, 5, 7, 6, 7, 7, 8, 7, 9, 8, 9, 9, 10, 9, 11, 10, 11, 11, 12, 11, 13, 12, 13, 13, 14, 13, 15, 14, 15, 15, 16, 15, 17, 16, 17, 17, 18, 17, 19, 18, 19, 19, 20, 19, 21, 20, 21, 21, 22, 21, 23, 22, 23, 23, 24, 23, 25, 24, 25, 25
Offset: 0

Views

Author

José María Grau Ribas, Jan 20 2016

Keywords

Links

Crossrefs

Cf. A000045, A267807, A267808, A267809.

Programs

  • Mathematica
    RecurrenceTable[{a[0] == a[1] == 1, a[n] == Mod[a[n - 1], 2] + a[n - 2]}, a, {n, 80}]
Table[Floor[(n + 2)/3] + (1 + (-1)^n)/2, {n, 0, 80}] (* or *) LinearRecurrence[{0, 1, 1, 0, -1}, {1, 1, 2, 1, 3}, 80] (* Bruno Berselli, Jan 21 2016 *)
  • PARI
    a=vector(100); for(n=1, #a, if(n<3, a[n]=1, a[n]=a[n-1]%2+a[n-2])); a \\ Colin Barker, Jan 22 2016

Formula

From Bruno Berselli, Jan 21 2016: (Start)
G.f.: (1 + x + x^2 - x^3)/((1 + x)*(1 - x)^2*(1 + x + x^2)).
a(n) = a(n-2) + a(n-3) - a(n-5) for n>4.
a(n) = floor((n + 2)/3) + (1 + (-1)^n)/2. (End)
a(n) = A051274(n+2). - R. J. Mathar, May 02 2023

Extensions

Edited by Bruno Berselli, Jan 21 2016.

A267807 a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 3) + a(n-2).

Original entry on oeis.org

1, 1, 2, 3, 2, 5, 4, 6, 4, 7, 5, 9, 5, 11, 7, 12, 7, 13, 8, 15, 8, 17, 10, 18, 10, 19, 11, 21, 11, 23, 13, 24, 13, 25, 14, 27, 14, 29, 16, 30, 16, 31, 17, 33, 17, 35, 19, 36, 19, 37, 20, 39, 20, 41, 22, 42, 22, 43, 23, 45, 23, 47, 25, 48, 25, 49, 26, 51, 26, 53, 28
Offset: 0

Views

Author

José María Grau Ribas, Jan 20 2016

Keywords

Links

Crossrefs

Cf. A000045, A267806, A267808, A267809.

Programs

  • Mathematica
    RecurrenceTable[{a[0] == a[1] == 1, a[n] == Mod[a[n - 1], 3] + a[n - 2]}, a, {n, 90}]
LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, 1, 0, -1}, {1, 1, 2, 3, 2, 5, 4, 6, 4, 7}, 90] (* Bruno Berselli, Jan 21 2016 *)
  • PARI
    a=vector(100); for(n=1, #a, if(n<3, a[n]=1, a[n]=a[n-1]%3+a[n-2])); a \\ Colin Barker, Jan 22 2016

Formula

G.f.: (1 + x + x^2 + 2*x^3 + 2*x^5 + 2*x^6 + x^7 - x^8)/((1 - x)^2*(1 + x)^2* (1 + x^2)*(1 + x^4)). [Bruno Berselli, Jan 21 2016]
a(n) = a(n-2) + a(n-8) - a(n-10) for n>9. [Bruno Berselli, Jan 21 2016]

Extensions

Edited by Bruno Berselli, Jan 21 2016

A267808 a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 4) + a(n-2).

Original entry on oeis.org

1, 1, 2, 3, 5, 4, 5, 5, 6, 7, 9, 8, 9, 9, 10, 11, 13, 12, 13, 13, 14, 15, 17, 16, 17, 17, 18, 19, 21, 20, 21, 21, 22, 23, 25, 24, 25, 25, 26, 27, 29, 28, 29, 29, 30, 31, 33, 32, 33, 33, 34, 35, 37, 36, 37, 37, 38, 39, 41, 40, 41, 41, 42, 43, 45, 44, 45, 45, 46, 47, 49
Offset: 0

Views

Author

José María Grau Ribas, Jan 20 2016

Keywords

Links

Crossrefs

Cf. A000045, A267806, A267807, A267809.

Programs

  • Mathematica
    RecurrenceTable[{a[0] == a[1] == 1, a[n] == Mod[a[n - 1], 4] + a[n - 2]}, a, {n, 70}]
Table[n - Floor[(n + 1)/3] + ((-1)^n - (-1)^Floor[n/3])/2 + 1, {n, 0, 70}] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 1, 2, 3, 5, 4, 5}, 80] (* Bruno Berselli, Jan 21 2016 *)
  • PARI
    a=vector(100); for(n=1, #a, if(n<3, a[n]=1, a[n]=a[n-1]%4+a[n-2])); a \\ Colin Barker, Jan 22 2016

Formula

From Bruno Berselli, Jan 21 2016: (Start)
G.f.: (1 + x^2 + x^3 + 2*x^4 - x^5) / ((1 + x)*(1 - x)^2*(1 - x + x^2)*(1 + x + x^2)).
a(n) = a(n-1) + a(n-6) - a(n-7) for n>6.
a(n) = n - floor((n+1)/3) + ((-1)^n - (-1)^(floor(n/3)))/2 + 1. (End)

Extensions

Edited by Bruno Berselli, Jan 21 2016.

A300999 Add to a(n) the first digit of a(n+1) to get a(n+2), with a(1) = 1 and a(2) = 2.

Original entry on oeis.org

1, 2, 3, 5, 8, 13, 9, 22, 11, 23, 13, 24, 15, 25, 17, 26, 19, 27, 21, 29, 23, 31, 26, 33, 29, 35, 32, 38, 35, 41, 39, 44, 43, 48, 47, 52, 52, 57, 57, 62, 63, 68, 69, 74, 76, 81, 84, 89, 92, 98, 101, 99, 110, 100, 111, 101, 112, 102, 113, 103, 114, 104, 115, 105, 116, 106, 117, 107, 118, 108, 119
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Mar 20 2018

Keywords

Comments

The sequence, starting with a(1) = 1 and a(2) = 2, never enters into a loop.

Examples

			a(1) + first digit of a(2) =  1 + 2 = a(3) =  3,
a(2) + first digit of a(3) =  2 + 3 = a(4) =  5,
a(3) + first digit of a(4) =  3 + 5 = a(5) =  8,
a(4) + first digit of a(5) =  5 + 8 = a(6) = 13,
a(5) + first digit of a(6) =  8 + 1 = a(7) =  9,
a(6) + first digit of a(7) = 13 + 9 = a(8) = 22,
a(7) + first digit of a(8) =  9 + 2 = a(9) = 11,
etc.

Links

Crossrefs

Cf. A267809.

Programs

  • Mathematica
    nxt[{a_,b_}]:={b,a+IntegerDigits[b][[1]]}; NestList[nxt,{1,2},80][[;;,1]] (* Harvey P. Dale, Nov 19 2023 *)
  • PARI
    a=vector(10^4); a[1]=1; a[2]=2; for(n=3, #a, a[n]=digits(a[n-1])[1]+a[n-2]); a \\ Altug Alkan, Mar 20 2018
Showing 1-4 of 4 results.

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

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