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 1-9 of 9 results.

A050042 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 1.

Original entry on oeis.org

1, 2, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 20, 25, 32, 40, 41, 43, 44, 46, 50, 55, 62, 70, 80, 91, 104, 118, 134, 154, 179, 211, 212, 214, 215, 217, 221, 226, 233, 241, 251, 262, 275, 289, 305, 325, 350, 382
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences, with different initial conditions, listed in A050034.

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)
  • PARI
    lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 1; for(n=4, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ Petros Hadjicostas, May 15 2020

Extensions

Name edited by Petros Hadjicostas, May 15 2020

A050046 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 2.

Original entry on oeis.org

1, 2, 2, 3, 5, 6, 8, 10, 13, 14, 16, 18, 21, 26, 32, 40, 50, 51, 53, 55, 58, 63, 69, 77, 87, 100, 114, 130, 148, 169, 195, 227, 267, 268, 270, 272, 275, 280, 286, 294, 304, 317, 331, 347, 365, 386, 412, 444
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences listed in A050034.

Programs

  • Maple
    a := proc(n) option remember;
     `if`(n < 4, [1, 2, 2][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Apr 23 2020
  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 2}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Apr 23 2020

A050054 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 4.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 14, 19, 20, 22, 26, 31, 38, 46, 56, 70, 71, 73, 77, 82, 89, 97, 107, 121, 140, 160, 182, 208, 239, 277, 323, 379, 380, 382, 386, 391, 398, 406, 416, 430, 449, 469, 491, 517, 548, 586, 632
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences with different initial conditions listed in A050034.

Programs

  • Maple
    a := proc(n) option remember;
     `if`(n < 4, [1, 2, 4][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 18 2019
  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 4}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 18 2019

A050058 a(n) = a(n-1)+a(m), where m=n-1-2^p and 2^p= 4.

Original entry on oeis.org

1, 3, 1, 2, 5, 6, 9, 10, 12, 13, 16, 17, 19, 24, 30, 39, 49, 50, 53, 54, 56, 61, 67, 76, 86, 98, 111, 127, 144, 163, 187, 217, 256, 257, 260, 261, 263, 268, 274, 283, 293, 305, 318, 334, 351, 370, 394, 424
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences, with different initial conditions, listed in A050034.

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

A050062 a(n) = a(n-1)+a(m), where m=n-1-2^p and 2^p= 4.

Original entry on oeis.org

1, 3, 2, 3, 6, 7, 10, 12, 15, 16, 19, 21, 24, 30, 37, 47, 59, 60, 63, 65, 68, 74, 81, 91, 103, 118, 134, 153, 174, 198, 228, 265, 312, 313, 316, 318, 321, 327, 334, 344, 356, 371, 387, 406, 427, 451, 481, 518
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences, with different initial conditions, listed in A050034.

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 2}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

A050066 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

Original entry on oeis.org

1, 3, 3, 4, 7, 8, 11, 14, 18, 19, 22, 25, 29, 36, 44, 55, 69, 70, 73, 76, 80, 87, 95, 106, 120, 138, 157, 179, 204, 233, 269, 313, 368, 369, 372, 375, 379, 386, 394, 405, 419, 437, 456, 478, 503, 532, 568, 612
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences with different initial conditions listed in A050034.

Programs

  • Maple
    a := proc(n) option remember;
     `if`(n < 4, [1, 3, 3][n], a(n - 1) + a(-2^ceil(-1+log[2](n - 1)) + n - 1)):
     end proc:
seq(a(n), n = 1..40); #
  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 3}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

Extensions

Name edited by Petros Hadjicostas, Nov 18 2019

A050070 a(n) = a(n-1)+a(m), where m=n-1-2^p and 2^p= 4.

Original entry on oeis.org

1, 3, 4, 5, 8, 9, 12, 16, 21, 22, 25, 29, 34, 42, 51, 63, 79, 80, 83, 87, 92, 100, 109, 121, 137, 158, 180, 205, 234, 268, 310, 361, 424, 425, 428, 432, 437, 445, 454, 466, 482, 503, 525, 550, 579, 613, 655
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences, with different initial conditions, listed in A050034.

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 4}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)

A050038 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.

Original entry on oeis.org

1, 1, 4, 5, 6, 7, 8, 12, 17, 18, 19, 23, 28, 34, 41, 49, 61, 62, 63, 67, 72, 78, 85, 93, 105, 122, 140, 159, 182, 210, 244, 285, 334, 335, 336, 340, 345, 351, 358, 366, 378, 395, 413, 432, 455, 483, 517, 558
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences with different initial conditions: A050026 (1,1,1), A050030 (1,1,2), A050034 (1,1,3), A050038 (1,1,4), A050042 (1,2,1), A050046 (1,2,2), A050054 (1,2,4), A050058 (1,3,1), A050062 (1,3,2), A050066 (1,3,3), A050070 (1,3,4).

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 4}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)
  • PARI
    lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 4; for(n=4, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ Petros Hadjicostas, May 15 2020

Extensions

Name edited by Petros Hadjicostas, May 15 2020

A050050 a(n) = a(n-1)+a(m), where m=n-1-2^p and 2^p= 4.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 12, 16, 17, 19, 22, 26, 32, 39, 48, 60, 61, 63, 66, 70, 76, 83, 92, 104, 120, 137, 156, 178, 204, 236, 275, 323, 324, 326, 329, 333, 339, 346, 355, 367, 383, 400, 419, 441, 467, 499, 538
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. similar sequences with different initial conditions: A050026 (1,1,1), A050030 (1,1,2), A050034 (1,1,3), A050038 (1,1,4), A050042 (1,2,1), A050046 (1,2,2), A050054 (1,2,4), A050058 (1,3,1), A050062 (1,3,2), A050066 (1,3,3), A050070 (1,3,4).

Programs

  • Mathematica
    Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 3}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 08 2015 *)
Showing 1-9 of 9 results.

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