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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A190853 Integers in (A190809)/2; contains A190809 as a proper subsequence.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 20, 22, 25, 26, 28, 31, 32, 34, 40, 43, 44, 49, 50, 52, 53, 56, 61, 62, 64, 67, 68, 76, 79, 80, 85, 86, 88, 94, 97, 98, 100, 103, 104, 106, 112, 121, 122, 124, 128, 130, 133, 134, 136, 148, 151, 152, 157, 158, 160, 161, 169, 170, 172, 176, 184, 187, 188, 193, 194, 196, 200, 202, 205, 206, 208, 212
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190809, A190854.

Programs

A190854 Integers in (-2+A190809)/3; contains A190809 as a proper subsequence.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 10, 14, 16, 17, 18, 20, 22, 26, 28, 32, 34, 40, 42, 44, 50, 52, 53, 56, 58, 62, 64, 66, 68, 70, 74, 80, 82, 86, 88, 90, 98, 100, 104, 106, 112, 114, 122, 124, 128, 130, 134, 136, 138, 152, 158, 160, 161, 162, 170, 172, 176, 178, 188, 194, 196, 200, 202, 206, 208, 210, 212, 214, 224, 226, 234, 242, 244, 248, 250, 256
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190909, A190853.

Programs

A190858 Integers in (-1+A002977)/2; contains A002977 as a proper subsequence.

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 33, 39, 40, 42, 43, 45, 46, 55, 57, 58, 60, 63, 64, 67, 69, 79, 81, 82, 85, 87, 91, 93, 94, 96, 111, 115, 117, 118, 121, 123, 127, 129, 130, 135, 136, 139, 141, 159, 163, 165, 166, 171, 172, 175, 177, 183, 187, 189, 190, 193, 195, 202, 204, 223, 231, 235, 237, 238, 243, 244, 247, 249
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A002977, A190859.

Programs

  • Mathematica
    h = 2; i = 1; j = 3; k = 1; f = 1; g = 9 ;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A002977 *)
b = (a - 1)/2; c = (a - 1)/3; r = Range[1, 300];
d = Intersection[b, r] (* A190858 *)
e = Intersection[c, r] (* A190859 *)

A190812 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x+1 and 3x+2 are in a.

Original entry on oeis.org

1, 3, 5, 7, 11, 15, 17, 23, 31, 35, 47, 53, 63, 71, 95, 107, 127, 143, 161, 191, 215, 255, 287, 323, 383, 431, 485, 511, 575, 647, 767, 863, 971, 1023, 1151, 1295, 1457, 1535, 1727, 1943, 2047, 2303, 2591, 2915, 3071, 3455, 3887, 4095, 4373, 4607, 5183, 5831, 6143, 6911, 7775, 8191, 8747, 9215, 10367, 11663
Offset: 1

Views

Author

Clark Kimberling, May 20 2011

Keywords

Comments

See A190803.

Links

Crossrefs

Cf. A190803, A069353, A190812.

Programs

  • Haskell
    import Data.Set (singleton, deleteFindMin, insert)
a190812 n = a190812_list !! (n-1)
a190812_list = f $ singleton 1
   where f s = m : (f $ insert (2*m+1) $ insert (3*m+2) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011
  • Mathematica
    h = 2; i = 1; j = 3; k = 2; f = 1; g = 20 ;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190812 *)
b = (a - 1)/2; c = (a - 2)/3; r = Range[1, 30000];
d = Intersection[b, r] (* A069353 *)
e = Intersection[c, r] (* A190812 conjectured *)

Extensions

a(41)=2047 inserted by Reinhard Zumkeller, Jun 01 2011

A190845 Integers in (1+A190805)/2; contains A190805 as a proper subsequence.

Original entry on oeis.org

1, 4, 7, 13, 22, 25, 34, 40, 43, 49, 61, 67, 76, 79, 85, 97, 115, 121, 130, 133, 148, 151, 157, 169, 193, 196, 202, 223, 229, 238, 241, 256, 259, 265, 292, 295, 301, 304, 313, 337, 358, 364, 385, 391, 400, 403, 439, 445, 454, 457, 472, 475, 481
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190805.

Programs

A190848 Integers in (-2+A190806)/3; contains A190806 as a proper subsequence.

Original entry on oeis.org

1, 5, 9, 17, 21, 29, 33, 37, 53, 57, 65, 69, 85, 89, 101, 105, 113, 117, 129, 133, 149, 161, 173, 177, 197, 201, 209, 213, 225, 229, 257, 261, 269, 277, 305, 317, 321, 341, 345, 353, 357, 389, 393, 401, 405, 417, 421, 449, 453, 469, 485, 513, 517, 521, 533, 537, 593, 597, 605, 609, 629, 633, 641, 645, 677, 681, 689, 693, 705, 709
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190806.

Programs

A190855 Integers in (-1+A190810)/2; contains A190810 as a proper subsequence.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 11, 14, 15, 17, 20, 23, 29, 31, 32, 35, 41, 44, 47, 50, 59, 63, 65, 68, 71, 74, 83, 86, 89, 92, 95, 101, 104, 119, 122, 127, 128, 131, 137, 140, 143, 149, 155, 167, 173, 176, 179, 182, 185, 188, 191, 194, 203, 209, 212, 239, 245, 248, 255, 257, 263, 266, 275, 281, 284, 287, 290, 299, 302, 311, 317, 335, 347, 353, 356
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190810, A190856.

Programs

A190857 Integers in (A190811)/3; contains A190811 as a proper subsequence.

Original entry on oeis.org

1, 3, 5, 7, 9, 13, 15, 19, 21, 27, 29, 31, 37, 39, 43, 45, 53, 55, 57, 61, 63, 77, 79, 81, 85, 87, 91, 93, 109, 111, 115, 117, 125, 127, 129, 135, 149, 157, 159, 163, 165, 171, 173, 175, 181, 183, 187, 189, 213, 221, 223, 229, 231, 235, 237, 243, 245, 253, 255, 259, 261, 271, 273, 279
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A190811.

Programs

A190859 Integers in (-1+A002977)/3; contains A002977 as a proper subsequence.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 10, 13, 14, 15, 18, 19, 21, 22, 26, 27, 28, 30, 31, 38, 39, 40, 42, 43, 45, 46, 54, 55, 57, 58, 62, 63, 64, 67, 74, 78, 79, 81, 82, 85, 86, 87, 90, 91, 93, 94, 106, 110, 111, 114, 115, 117, 118, 121, 122, 126, 127, 129, 130, 135, 136, 139, 154, 158, 159, 162, 163, 165, 166, 170, 171, 172, 174, 175, 182, 183, 186
Offset: 1

Views

Author

Clark Kimberling, May 25 2011

Keywords

Comments

See A190803.

Crossrefs

Cf. A190803, A002977, A190858.

Programs

A191109 a(1)=1, and if x is a term then 3x-1 and 3x+2 are terms too.

Original entry on oeis.org

1, 2, 5, 8, 14, 17, 23, 26, 41, 44, 50, 53, 68, 71, 77, 80, 122, 125, 131, 134, 149, 152, 158, 161, 203, 206, 212, 215, 230, 233, 239, 242, 365, 368, 374, 377, 392, 395, 401, 404, 446, 449, 455, 458, 473, 476, 482, 485, 608, 611, 617, 620, 635, 638, 644, 647, 689, 692, 698, 701, 716, 719, 725, 728, 1094, 1097, 1103, 1106, 1121
Offset: 1

Views

Author

Clark Kimberling, May 26 2011

Keywords

Comments

See discussions at A190803, A191106.
The positive integers in (1+A191109)/3 comprise A153775, a proper subsequence of A191109.
The positive integers in (-2+A191109)/3 comprise A032924, a proper subsequence of A191109.

Links

Crossrefs

Cf. A190803, A191106, A153775, A032924.

Programs

  • Mathematica
    h = 3; i = -1; j = 3; k = 2; f = 1;  g = 7;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* 191109 *)
b = (a + 1)/3; c = (a - 2)/3; r = Range[1, 900];
d = Intersection[b, r] (* A153775 *)
e = Intersection[c, r] (* A032924 *)
Nest[Flatten[{#,3#-1,3#+2}]&,1,10]//Union (* Harvey P. Dale, Apr 05 2020 *)

Extensions

Name edited by Michel Marcus, Jul 29 2021
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