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.

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A108567 a(0) = 0, a(1) = a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 8, a(6) = 16, for n>5: a(n+1) = SORT[ a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6)], where SORT places digits in ascending order and deletes 0's.

Original entry on oeis.org

0, 1, 1, 2, 4, 8, 16, 23, 55, 19, 127, 225, 347, 128, 249, 115, 112, 133, 139, 1223, 299, 227, 2248, 1348, 1567, 157, 679, 2556, 2788, 11334, 2249, 1233, 2699, 23358, 12467, 12568, 5689, 2366, 368, 15559, 23577, 24579, 4678, 16678, 5788, 12279, 11338
Offset: 0

Views

Author

Jonathan Vos Post, Jun 11 2005

Keywords

Comments

T. D. Noe found that the maximum is attained at a(4992871827) = 234444568999. The periodic part of this sequence begins at a(3544675600) and has length 5158842780.

Examples

			a(7) = SORT[a(0) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6)] = SORT[0 + 1 + 1 + 2 + 4 + 8 + 16] = SORT[32] = 23.
a(8) = SORT[a(1) + a(2) + a(3) + a(4) + a(5) + a(6) + a(7)] = SORT[1 + 1 + 2 + 4 + 8 + 16 + 23] = SORT[55] = 55.
a(9) = SORT[a(2) + a(3) + a(4) + a(5) + a(6) + a(7) + a(8)] = SORT[1 + 2 + 4 + 8 + 16 + 23 + 55] = SORT[109] = 19.

Links

Crossrefs

Cf. A066178, A069638, A107281, A108564-A108566, A108568-A108573.

Programs

  • Mathematica
    nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,FromDigits[Sort[ IntegerDigits[ a+b+c+d+e+f+g]/.(0->Nothing)]]}; NestList[nxt,{0,1,1,2,4,8,16},50][[All,1]] (* Harvey P. Dale, May 09 2020 *)

A111430 Tribonacci(heptanacci(n)).

Original entry on oeis.org

0, 0, 1, 2, 24, 3136, 53798080, 15832480722303616, 745527911414639917440582097294401, 1653079675982713719400420113305863285438472194540328413077493166464
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			Heptanacci(10) = A066178(10) = 504, so tribonacci(heptanacci(10)) =
A000073(504) ~ 4.4 * 10^133.

Crossrefs

Cf. A000073, A066178, A007570.

Formula

a(n) = A000073(A066178(n)).

A111432 Fibonacci(tetranacci(n)).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 3, 21, 610, 514229, 225851433717, 16641027750620563662096, 13180872826374098837632191485015125807374171, 284812298108489611757988937681460995615380088782304890986477195645969271404032323901
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(tetranacci(0)) = A000045(A000078(0)) = A000045(0) = 0.
a(1) = Fibonacci(tetranacci(1)) = A000045(A000078(1)) = A000045(0) = 0.
a(2) = Fibonacci(tetranacci(2)) = A000045(A000078(2)) = A000045(0) = 0.
a(3) = Fibonacci(tetranacci(3)) = A000045(A000078(3)) = A000045(1) = 1.
a(4) = Fibonacci(tetranacci(4)) = A000045(A000078(4)) = A000045(1) = 1.
a(5) = A000045(A000078(5)) = A000045(2) = 1.
a(6) = A000045(A000078(6)) = A000045(4) = 3.
a(7) = A000045(A000078(7)) = A000045(8) = 21.
a(8) = A000045(A000078(8)) = A000045(15) = 610.
a(9) = A000045(A000078(9)) = A000045(29) = 514229.
a(10) = A000045(A000078(10)) = A000045(56) = 225851433717.

Crossrefs

Cf. A000045, A000078, A066178, A007570.

Programs

  • Mathematica
    Fibonacci[LinearRecurrence[{1,1,1,1},{0,0,0,1},14]] (* Harvey P. Dale, Aug 03 2017 *)

Formula

a(n) = A000045(A000078(n)).

A111433 Fibonacci(pentanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 3, 21, 987, 1346269, 2504730781961, 5358359254990966640871840, 9366947731425726508977331996039353971111632790877, 4176188314410464025148116525118839856571907649518456624120477965205524606115754507996484677228773
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(pentanacci(0)) = A000045(A001591(0)) = A000045(0) = 0.
a(1) = Fibonacci(pentanacci(1)) = A000045(A001591(1)) = A000045(0) = 0.
a(2) = Fibonacci(pentanacci(2)) = A000045(A001591(2)) = A000045(0) = 0.
a(3) = Fibonacci(pentanacci(3)) = A000045(A001591(3)) = A000045(0) = 0.
a(4) = Fibonacci(pentanacci(4)) = A000045(A001591(4)) = A000045(1) = 1.
a(5) = Fibonacci(pentanacci(5)) = A000045(A001591(5)) = A000045(1) = 1.
a(6) = Fibonacci(pentanacci(6)) = A000045(A001591(6)) = A000045(2) = 1.
a(7) = A000045(A001591(7)) = A000045(4) = 3.
a(8) = A000045(A001591(8)) = A000045(8) = 21.
a(9) = A000045(A001591(9)) = A000045(16) = 987.

Crossrefs

Cf. A000045, A001591, A066178, A007570.

Formula

a(n) = A000045(A001591(n)).

A111435 a(n) = Fibonacci(hexanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 3, 21, 987, 2178309, 6557470319842, 59425114757512643212875125, 3016128079338728432528443992613633888712980904400501
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(hexanacci(0)) = A000045(A001592(0)) = A000045(0) = 0.
a(1) = Fibonacci(hexanacci(1)) = A000045(A001592(1)) = A000045(0) = 0.
a(2) = Fibonacci(hexanacci(2)) = A000045(A001592(2)) = A000045(0) = 0.
a(3) = Fibonacci(hexanacci(3)) = A000045(A001592(3)) = A000045(0) = 0.
a(4) = Fibonacci(hexanacci(4)) = A000045(A001592(4)) = A000045(0) = 0.
a(5) = Fibonacci(hexanacci(5)) = A000045(A001592(5)) = A000045(1) = 1.
a(6) = Fibonacci(hexanacci(6)) = A000045(A001592(6)) = A000045(1) = 1.
a(7) = Fibonacci(hexanacci(7)) = A000045(A001592(7)) = A000045(2) = 1.
a(8) = A000045(A001592(8)) = A000045(4) = 3.
a(9) = A000045(A001592(9)) = A000045(8) = 21.
a(10) = A000045(A001592(10)) = A000045(16) = 987.
a(11) = A000045(A001592(11)) = A000045(32) = 2178309.
a(12) = A000045(A001592(12)) = A000045(63) = 6557470319842.

Crossrefs

Cf. A000045, A001592, A066178, A007570.

Programs

  • Maple
    b:= proc(n) option remember; `if`(n<5, 0,
      `if`(n=5, 1, add(b(n-j), j=1..6)))
    end:
a:= n-> (<<0|1>, <1|1>>^b(n))[1,2]:
seq(a(n), n=0..14);  # Alois P. Heinz, Aug 09 2018

Formula

a(n) = A000045(A001592(n)).

A111438 Fibonacci(heptanacci(n)), restricted to nonzero heptanacci numbers.

Original entry on oeis.org

1, 1, 1, 3, 21, 987, 2178309, 10610209857723, 155576970220531065681649693, 33449372971981195681356806732944396691005381570580873
Offset: 0

Views

Author

Jonathan Vos Post, Nov 14 2005

Keywords

Examples

			a(0) = Fibonacci(heptanacci(0)) = A000045(A066178(0)) = A000045(1) = 1.
a(1) = Fibonacci(heptanacci(1)) = A000045(A066178(1)) = A000045(1) = 1.
a(2) = Fibonacci(heptanacci(2)) = A000045(A066178(2)) = A000045(2) = 1.
a(3) = Fibonacci(heptanacci(3)) = A000045(A066178(3)) = A000045(4) = 3.
a(4) = Fibonacci(heptanacci(4)) = A000045(A066178(4)) = A000045(8) = 21.
a(5) = Fibonacci(heptanacci(5)) = A000045(A066178(5)) = A000045(16) = 987.
a(6) = A000045(A066178(6)) = A000045(32) = 2178309.
a(7) = A000045(A066178(7)) = A000045(64) = 10610209857723.
a(8) = A000045(A066178(8)) = A000045(127) = 155576970220531065681649693.

Crossrefs

Cf. A000045, A001592, A066178, A007570.

Formula

a(n) = A000045(A066178(n)).

Extensions

Corrected by T. D. Noe, Nov 16 2006
Previous Showing 21-26 of 26 results.

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