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.

Previous Showing 71-79 of 79 results.

A120195 a(1)=2; a(n) = floor((17 + Sum_{j=1..n-1} a(j))/8).

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 25, 28, 32, 36, 40, 45, 51, 57, 64, 72, 81, 92, 103, 116, 130, 147, 165, 186, 209, 235, 264, 297, 335, 376, 423, 476, 536, 603, 678, 763, 858, 966, 1086, 1222, 1375, 1547, 1740, 1958, 2202
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    f[s_] := Append[s, Floor[(17 + Plus @@ s)/8]]; Nest[f, {2}, 60] (* Robert G. Wilson v, Jul 08 2006 *)

Extensions

More terms from Robert G. Wilson v, Jul 08 2006

A120196 a(1)=3; a(n) = floor((26 + Sum_{j=1..n-1} a(j))/8).

Original entry on oeis.org

3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 12, 13, 15, 17, 19, 21, 24, 27, 30, 34, 38, 43, 48, 54, 61, 69, 77, 87, 98, 110, 124, 139, 157, 176, 198, 223, 251, 282, 318, 357, 402, 452, 509, 572, 644, 724, 815, 917, 1031, 1160, 1305, 1468, 1652, 1858, 2091, 2352, 2646, 2977
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Mathematica
    a[1] = 3; a[n_] := a[n] = Floor[(26 + Sum[a[j], {j, n - 1}])/8]; Table[
a@ n, {n, 60}] (* Michael De Vlieger, Nov 29 2015 *)
  • PARI
    lista(nn) = {va = vector(nn); va[1] = 3; for (n=2, nn, va[n] = (26 + sum(j=1, n-1, va[j]))\8;); va;} \\ Michel Marcus, Nov 29 2015

Extensions

More terms from Michel Marcus, Nov 29 2015

A120197 a(1)=4; a(n)=floor((35+sum(a(1) to a(n-1)))/8).

Original entry on oeis.org

4, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 23, 26, 29, 33, 37, 41, 46, 52, 59, 66, 74, 84, 94, 106, 119, 134, 151, 170, 191, 215, 242, 272, 306, 344, 387
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

A120198 a(1)=5; a(n)=floor((44+sum(a(1) to a(n-1)))/8).

Original entry on oeis.org

5, 6, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 23, 26, 29, 33, 37, 41, 47, 52, 59, 66, 75, 84, 94, 106, 119, 134, 151, 170, 191, 215, 242, 272, 306, 344, 387, 436, 490
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

A120205 a(1) = 4; a(n) = floor((39 + Sum_{i=1..n-1} a(i))/9).

Original entry on oeis.org

4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 21, 23, 26, 29, 32, 35, 39, 44, 49, 54, 60, 67, 74, 82, 91, 102, 113, 125, 139, 155, 172, 191, 212, 236, 262, 291, 324, 360, 400, 444, 493, 548, 609, 677, 752, 835, 928, 1031, 1146, 1273, 1415, 1572
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    Module[{ll={4}},Do[AppendTo[ll,Floor[(39+Total[ll])/9]],{60}];ll] (* Harvey P. Dale, May 07 2012 *)

Extensions

More terms from Harvey P. Dale, May 07 2012

A120207 a(1)=6; a(n)=floor((59+sum(a(1) to a(n-1)))/9).

Original entry on oeis.org

6, 7, 8, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 24, 26, 29, 33, 36, 40, 45, 50, 55, 61, 68, 76, 84, 93, 104, 115, 128, 142, 158, 176, 195, 217, 241, 268, 298, 331, 367
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

A120208 a(1)=7; a(n)=floor((69+sum(a(1) to a(n-1)))/9).

Original entry on oeis.org

7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 21, 23, 26, 29, 32, 35, 39, 44, 48, 54, 60, 66, 74, 82, 91, 101, 112, 125, 139, 154, 171, 190, 211, 235, 261, 290, 322, 358, 398, 442, 491, 546, 606, 674, 749, 832, 924, 1027, 1141, 1268, 1409, 1565, 1739, 1932, 2147
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    Module[{lst={7}},Do[AppendTo[lst,Floor[(69+Total[lst])/9]],{80}];lst] (* Harvey P. Dale, Aug 14 2012 *)

Extensions

More terms from Harvey P. Dale, Aug 14 2012

A333589 a(n) = floor(a(n-1)*3/2) bitwise-OR LSB(a(n-1)*n), with a(1)=2 (LSB = Least Significant Bit).

Original entry on oeis.org

2, 3, 5, 7, 11, 16, 24, 36, 54, 81, 121, 181, 271, 406, 609, 913, 1369, 2053, 3079, 4618, 6927, 10390, 15585, 23377, 35065, 52597, 78895, 118342, 177513, 266269, 399403, 599104, 898656, 1347984, 2021976, 3032964, 4549446, 6824169, 10236253, 15354379, 23031569, 34547353, 51821029, 77731543, 116597315
Offset: 1

Views

Author

Simon Strandgaard, Mar 27 2020

Keywords

Examples

			even index = x + (x>>1)
odd index = (x + (x>>1)) | least significant bit of x
3 = 2 + 1
5 = (3 + 1) | 1
7 = 5 + 2
11 = (7 + 3) | 1
16 = 11 + 5
24 = (16 + 8) | 0
36 = 24 + 12
54 = (36 + 18) | 0
81 = 54 + 27
121 = (81 + 40) | 1

Crossrefs

Cf. A112088, A333588.

Programs

  • Mathematica
    a[1] = 2; a[n_] := a[n] = BitOr[Floor[a[n - 1]*3/2], Mod[a[n - 1]*n, 2]]; Array[a, 45] (* Amiram Eldar, May 01 2020 *)
  • PARI
    lista(nn) = {my(a=2, va = List(a)); for (n=2, nn, my(x = a + a>>1); if (n%2, a = bitor(x, a%2), a = x); listput(va, a);); Vec(va);} \\ Michel Marcus, May 03 2020
  • Ruby
    values = [2]; 100.times { |index| x = values.last; values << ((x + (x>>1)) | (x&1&index)) }; p values

Formula

a(n) = floor(a(n-1)*3/2) bitwise-OR LSB(a(n-1)*n), with a(1)=2 (LSB = Least Significant Bit).

A381677 a(n) = floor(a(n-1)*3/2) with a(1) = 5.

Original entry on oeis.org

5, 7, 10, 15, 22, 33, 49, 73, 109, 163, 244, 366, 549, 823, 1234, 1851, 2776, 4164, 6246, 9369, 14053, 21079, 31618, 47427, 71140, 106710, 160065, 240097, 360145, 540217, 810325, 1215487, 1823230, 2734845, 4102267, 6153400, 9230100, 13845150, 20767725, 31151587, 46727380, 70091070, 105136605, 157704907
Offset: 1

Views

Author

Juan Martin Rodriguez, Mar 03 2025

Keywords

Comments

The final number of animals if at each step two animals are bred and produce one offspring, starting with 5 animals (as in the game Minecraft, and waiting for all animals to be fully grown before the next round of breeding).

Examples

			a(3) = floor(a(2)/2)+a(2) = floor(7/2)+7 = 3+7 = 10.

Crossrefs

Cf. A032766, A061418.
Cf. A112088 (first differences).

Programs

  • Java
    class Main {
    public static void main(String[] args) {
        long a=5; // if you need more than 103 terms, you will need to use BigInteger
        System.out.print(a);
        for(int n = 0; n<104;n++){
            a += a/2;
            System.out.print(","+a);
        }
    }
}
  • Mathematica
    a[1]=5;a[n_]:=Floor[(a[n-1]*3/2)];Array[a,44] (* James C. McMahon, Mar 08 2025 *)
  • PARI
    lista(n)= my(t=10/3); vector(n, i, t=t*3\2) \\ Ruud H.G. van Tol, Mar 09 2025
Previous Showing 71-79 of 79 results.

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