A030777 -id:A030777 - cp's OEIS frontend

A030729 Number of new terms at stage n in the formation of A030727; likewise at stage n in the formation of A030777.

1, 2, 3, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 22, 24, 27, 30, 35, 38, 41, 44, 46, 49, 52, 58, 61, 63, 67, 72, 75, 80, 83, 85, 88, 93, 97, 102, 105, 106, 112, 115, 121, 126, 131, 133, 136, 140, 144, 150, 156, 160, 165, 170, 174, 180, 184, 187, 192, 198, 206, 211

Offset: 1

Clark Kimberling

nonn

Cf. A030727, A030777.

More terms from Sean A. Irvine, Apr 08 2020

A030780 a(n) is the least k such that A030777(k) = n.

Original entry on oeis.org

2, 3, 1, 14, 10, 8, 13, 20, 22, 29, 40, 31, 54, 190, 42, 68, 85, 55, 122, 146, 70, 170, 169, 87, 227, 195, 106, 225, 226, 126, 261, 148, 299, 172, 228, 526, 199, 340, 585, 263, 229, 301, 530, 264, 430, 776, 710, 342, 479, 302, 532, 386, 531, 343, 432, 1749

Offset: 1

Clark Kimberling

nonn

Cf. A030777.

Name clarified by Jinyuan Wang, Apr 08 2020

More terms from Sean A. Irvine, Apr 08 2020

A030781 Record values in A030777.

Original entry on oeis.org

3, 6, 7, 8, 9, 10, 12, 15, 18, 21, 24, 27, 30, 32, 34, 37, 41, 44, 50, 54, 58, 62, 65, 68, 72, 78, 82, 85, 90, 96, 100, 106, 110, 113, 117, 123, 128, 134, 138, 140, 145, 149, 155, 161, 167, 170, 174, 179, 183, 190, 197, 202, 208, 214, 219, 226, 231, 235, 241

Offset: 1

Clark Kimberling

nonn

More terms and simpler title from Sean A. Irvine, Apr 09 2020

A030782 Positions of record values in A030777.

Original entry on oeis.org

1, 8, 13, 20, 22, 29, 31, 42, 55, 70, 87, 106, 126, 148, 172, 199, 229, 264, 302, 343, 387, 433, 482, 534, 592, 653, 716, 783, 855, 930, 1010, 1093, 1178, 1266, 1359, 1456, 1558, 1663, 1769, 1881, 1996, 2117, 2243, 2374, 2507, 2643, 2783, 2927, 3077, 3233

Offset: 1

Clark Kimberling

nonn

More terms and simpler title from Sean A. Irvine, Apr 09 2020

A030783 s(k)=1, where s=A030777.

Original entry on oeis.org

2, 4, 6, 11, 12, 16, 19, 23, 24, 32, 33, 43, 45, 56, 58, 71, 73, 88, 91, 107, 127, 149, 154, 173, 178, 179, 200, 216, 230, 232, 236, 237, 240, 265, 267, 272, 303, 305, 311, 344, 346, 351, 388, 390, 434, 436, 483, 485, 491, 535, 537

Offset: 1

Clark Kimberling

nonn

A030784 s(n)=2, where s=A030777.

Original entry on oeis.org

3, 9, 18, 25, 28, 34, 35, 44, 57, 60, 72, 75, 89, 92, 108, 111, 128, 131, 150, 174, 181, 201, 205, 207, 208, 231, 266, 269, 274, 275, 278, 304, 307, 313, 345, 348, 389, 392, 397, 435, 438, 441, 484, 487, 536, 539, 547, 557, 594

Offset: 1

Clark Kimberling

nonn

A030785 Numbers k such that A030777(k) = 3.

Original entry on oeis.org

1, 5, 7, 17, 46, 47, 48, 133, 155, 210, 233, 239, 242, 251, 268, 306, 309, 315, 316, 319, 347, 350, 355, 357, 391, 394, 437, 440, 486, 489, 493, 538, 541, 596, 599, 607, 618, 657, 660, 666, 668, 674, 720, 723, 787, 790, 859, 862

Offset: 1

Clark Kimberling

nonn

Cf. A030777.

A030786 Numbers k such that A030777(k) = 4.

Original entry on oeis.org

14, 26, 27, 36, 59, 61, 63, 74, 77, 90, 94, 109, 112, 129, 151, 157, 175, 182, 202, 243, 270, 277, 280, 289, 308, 349, 353, 359, 360, 393, 401, 403, 439, 443, 446, 488, 540, 544, 549, 598, 659, 670, 722, 732, 734, 741, 745, 789

Offset: 1

Clark Kimberling

nonn

Cf. A030777.

A030717 The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

1, 1, 2, 2, 1, 3, 2, 3, 3, 1, 4, 3, 3, 4, 3, 5, 1, 5, 3, 6, 2, 1, 6, 4, 7, 2, 2, 1, 7, 6, 7, 3, 2, 2, 1, 8, 8, 8, 3, 2, 3, 3, 8, 9, 11, 3, 2, 3, 3, 3, 8, 10, 15, 3, 2, 3, 3, 4, 1, 1, 10, 11, 18, 4, 2, 3, 3, 5, 1, 1, 1, 1, 14, 12, 20, 5, 3, 3, 3, 5, 1, 2, 2, 1

Offset: 1

Clark Kimberling

The clarifying comment that follows refers to the old name, which was: Row 1, where, at stage k>1, write i in row 1 and j in row 2, where i is the number of j's in row 1, for j=1,2,...,m, where m=max number in row 1 from stages 1 to k-1; state 1 is 1 in row 1.

Numbers j for which the count is 0 are omitted, cf. A333867 for the corresponding sequence where they are included. - Sean A. Irvine, Apr 08 2020

			First list begins:
  1;
  1;
  2;
  2, 1;
  3, 2;
  3, 3,  1;
  4, 3,  3;
  4, 3,  5, 1;
  5, 3,  6, 2, 1;
  6, 4,  7, 2, 2, 1;
  7, 6,  7, 3, 2, 2, 1;
  8, 8,  8, 3, 2, 3, 3;
  8, 9, 11, 3, 2, 3, 3, 3;

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Sean A. Irvine)
Sean A. Irvine, Java program (github)

Cf. A030718 (2nd list), A030719 (row lengths), A006920.
Cf. A030707 (repeatedly adds values and frequencies from both lists).
Cf. A333867 (0 counts included, but not the counts of 0s).
Cf. A030723, A030724, A030725, A030726, A358423, A358424, A358425.

t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {25}];
DeleteCases[Flatten[t], 0]  (* Peter J. C. Moses, Apr 09 2020 *)

More terms from Franklin T. Adams-Watters, Dec 14 2006
Rolled back to original definition and data by Sean A. Irvine, Apr 08 2020
Name revised in line with A030777 by Peter Munn, Oct 11 2022

A030707 The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

1, 1, 3, 4, 1, 6, 2, 1, 8, 1, 3, 2, 1, 11, 3, 5, 3, 2, 1, 13, 5, 8, 4, 1, 3, 2, 1, 16, 7, 10, 6, 3, 4, 4, 2, 1, 18, 9, 12, 9, 4, 6, 1, 5, 1, 3, 2, 1, 22, 11, 14, 11, 6, 8, 2, 6, 2, 2, 4, 1, 3, 2, 1, 25, 16, 16, 13, 7, 11, 3, 8, 3, 3, 7, 2, 4, 1, 3, 2, 1, 28, 19, 21

Offset: 1

Clark Kimberling

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..1000
Sean A. Irvine, Java program (github)

Cf. A030708 (2nd list).

Name revised in line with A030777 by Peter Munn, Oct 08 2022

cp's OEIS Frontend

A030729 Number of new terms at stage n in the formation of A030727; likewise at stage n in the formation of A030777.

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A030780 a(n) is the least k such that A030777(k) = n.

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A030781 Record values in A030777.

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A030782 Positions of record values in A030777.

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A030783 s(k)=1, where s=A030777.

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A030784 s(n)=2, where s=A030777.

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A030785 Numbers k such that A030777(k) = 3.

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A030786 Numbers k such that A030777(k) = 4.

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A030717 The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030707 The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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