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 1-5 of 5 results.

A287118 Numbers k such that A284644(k) = A284644(k-1) = A284644(k-2) = A284644(k-3).

Original entry on oeis.org

84, 172, 348, 700, 1404, 2720, 2754, 5448, 10904, 21816, 43640, 87288
Offset: 1

Views

Author

Altug Alkan, following a suggestion from Nathan Fox, May 24 2017

Keywords

Comments

For the first twelve terms of this sequence, corresponding values of A284644(k) are 11*2^2, 11*2^3, 11*2^4, 11*2^5, 11*2^6, 11*31*2^2, 3*5*23*2^2, 11*31*2^3, 11*31*2^4, 11*31*2^5, 11*31*2^6, 11*31*2^7 and k - A284644(k) are 40, 84, 172, 348, 700, 1356, 1374, 2720, 5448, 10904, 21816, 43640.
Additionally, a(n) = 2*a(n-1) + 4 for 1 < n < 6 and a(n) = 2*a(n-1) + 8 for 8 < n < 13. In fact, also 5448 = 2720*2 + 8 but there is a(7) = 2754 between 2720 and 5448. In other words, we can partition sequence up to 10^5 as three subsequences: {84, 172, 348, 700, 1404}, {2754}, {2720, 5448, 10904, 21816, 43640, 87288} in order to see curious recursive patterns.
If a(13) exists, it must be greater than 7.5*10^9. - Hans Havermann, May 27 2017

Links

Crossrefs

Cf. A284644.

Programs

  • Mathematica
    a[1]=a[2]=2;a[3]=1;a[n_]:=a[n]=a[n-a[n-1]]+a[n-a[n-2]];SequencePosition[Table[a@n,{n,90000}],{x_,x_,x_,x_}][[;;,2]] (* Harvey P. Dale, Jul 16 2024 *)
  • PARI
    q=vector(10^8); q[1]=q[2]=2;q[3]=1; for(n=4, #q, q[n]=q[n-q[n-1]]+q[n-q[n-2]]); for (k=3, 10^8, if(q[k] == q[k-1] && q[k] == q[k-2] && q[k] == q[k-3], print1(k, ", ")));

A293947 Sequence P(n) arising in the analysis of the Hofstadter "brother" sequence A284644.

Original entry on oeis.org

1, 3, 8, 19, 41, 85, 173, 349, 701, 1405, 2800, 5576, 11128, 22221, 44342, 88422, 176507, 352062, 702831, 1403235, 2802382, 5598862, 11185734, 22353592, 44674558
Offset: 1

Views

Author

N. J. A. Sloane, Oct 26 2017

Keywords

Links

Crossrefs

Cf. A004001, A005185, A244477, A284644.

A296440 a(1) = 2, a(2) = a(3) = 3, a(4) = 4, a(5) = a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

Original entry on oeis.org

2, 3, 3, 4, 6, 6, 7, 8, 8, 9, 9, 10, 11, 13, 13, 12, 14, 16, 16, 14, 19, 17, 18, 19, 21, 21, 20, 22, 23, 24, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 34, 33, 34, 35, 37, 36, 37, 39, 36, 39, 42, 39, 41, 41, 44, 45, 41, 40, 50, 46, 48, 43, 48, 51, 49, 49, 54, 48, 53, 51, 58, 50, 58, 52, 57, 56, 59, 57, 60, 58
Offset: 1

Views

Author

Altug Alkan, Dec 12 2017

Keywords

Comments

Conjecture: Sequence is infinite.

Links

Crossrefs

Cf. A005185, A278055, A284644, A292351.

Programs

  • Maple
    a:= proc(n) option remember; procname(n-procname(n-1))+procname(n-procname(n-2))+procname(n-procname(n-3)) end proc:
a(1):= 2: a(2):= 3: a(3):= 3: a(4):= 4: a(5):= 6: a(6):= 6:
map(a, [$1..100]); # Robert Israel, Dec 12 2017
  • Mathematica
    a[n_] := a[n] = If[n<7, {2, 3, 3, 4, 6, 6}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 83] (* Giovanni Resta, Dec 13 2017 *)
  • PARI
    my(q=vector(100)); q[1]=2;q[2]=3;q[3]=3;q[4]=4;q[5]=6;q[6]=6; for(n=7, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q
  • Scheme
    ;; With memoization-macro definec.
(definec (A296440 n) (cond ((= 1 n) 2) ((<= n 3) 3) ((= 4 n) 4) ((<= n 6) 6) (else (+ (A296440 (- n (A296440 (- n 1)))) (A296440 (- n (A296440 (- n 2)))) (A296440 (- n (A296440 (- n 3)))))))) ;; Antti Karttunen, Dec 13 2017

A296421 a(1) = 1, a(2) = 2, a(3) = 3, a(4) = a(5) = 4, a(6) = a(7) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 7.

Original entry on oeis.org

1, 2, 3, 4, 4, 6, 6, 8, 7, 9, 9, 10, 11, 11, 12, 12, 14, 16, 13, 16, 16, 19, 16, 20, 17, 22, 19, 22, 21, 24, 22, 26, 22, 28, 24, 29, 26, 28, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 38, 40, 39, 38, 42, 41, 42, 44, 41, 43, 45, 51, 40, 44, 53, 46, 51, 44, 55, 47, 53, 54, 51, 55
Offset: 1

Views

Author

Altug Alkan, Dec 12 2017

Keywords

Links

Crossrefs

Cf. A005185, A284644, A278055, A292351.

Programs

  • Mathematica
    Fold[Append[#1, #1[[#2 - #1[[#2 - 1]] ]] + #1[[#2 - #1[[#2 - 2]] ]] + #1[[#2 - #1[[#2 - 3]] ]] ] &, {1, 2, 3, 4, 4, 6, 6}, Range[8, 75]] (* Michael De Vlieger, Dec 12 2017 *)
  • PARI
    q=vector(10^5); q[1]=1;q[2]=2;q[3]=3;q[4]=4;q[5]=4;q[6]=6;q[7]=6;for(n=8, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q

A296690 a(1) = a(2) = a(3) = 2, a(4) = 4, a(5) = a(6) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

Original entry on oeis.org

2, 2, 2, 4, 5, 5, 6, 6, 8, 10, 9, 8, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 20, 22, 21, 20, 24, 25, 20, 25, 28, 28, 21, 29, 32, 30, 25, 30, 30, 36, 30, 32, 35, 34, 36, 35, 37, 37, 38, 38, 40, 40, 40, 42, 41, 43, 43, 43, 45, 44, 46, 46, 47, 47, 49, 49, 49, 51, 50, 52, 52, 52, 54, 53, 56, 55, 58, 55, 62, 55
Offset: 1

Views

Author

Altug Alkan, Dec 18 2017

Keywords

Links

Crossrefs

Cf. A005185, A278055, A284644, A292351, A296413, A296421, A296440, A296518.

Programs

  • Maple
    a:= proc(n) option remember; procname(n-procname(n-1))+procname(n-procname(n-2))+procname(n-procname(n-3)) end proc:
a(1):= 2: a(2):= 2: a(3):= 2: a(4):= 4: a(5):= 5: a(6):= 5:
map(a, [$1..100]); #  after Robert Israel at A296440
  • Mathematica
    a[n_] := a[n] = If[n<7, {2, 2, 2, 4, 5, 5}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 100] (* after Giovanni Resta at A296440 *)
  • PARI
    q=vector(10^5); q[1]=2; q[2]=2; q[3]=2; q[4]=4; q[5]=5; q[6]=5; for(n=7, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q
  • Scheme
    (definec (A296690 n) (cond ((<= n 3) 2) ((<= n 5) n) ((= n 6) 5) (else (+ (A296690 (- n (A296690 (- n 1)))) (A296690 (- n (A296690 (- n 2)))) (A296690 (- n (A296690 (- n 3)))))))) ;; Antti Karttunen, Dec 18 2017
Showing 1-5 of 5 results.

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

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