A030707 -id:A030707 - cp's OEIS frontend

A030709 Number of new terms at stage n in the formation of A030707.

1, 1, 2, 3, 5, 6, 8, 9, 12, 15, 17, 18, 22, 24, 27, 30, 34, 36, 39, 42, 46, 48, 52, 57, 61, 65, 68, 71, 73, 77, 81, 84, 88, 92, 95, 99, 105, 108, 111, 114, 119, 124, 126, 130, 136, 142, 147, 150, 155, 158, 164, 167, 175, 180, 185, 189, 193, 197, 202, 207, 211

Offset: 1

Clark Kimberling

nonn

Also the number of new terms at stage n in the formation of A030757.

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

Cf. A030707, A030708, A030757, A030758.

More terms from Sean A. Irvine, Apr 06 2020

A030711 Record values in A030707.

Original entry on oeis.org

1, 3, 4, 6, 8, 11, 13, 16, 18, 22, 25, 28, 30, 35, 38, 42, 45, 50, 52, 56, 59, 64, 66, 71, 77, 82, 87, 91, 95, 97, 102, 107, 111, 116, 121, 125, 128, 135, 139, 143, 147, 152, 158, 161, 166, 172, 178, 184, 188, 194, 198, 205, 209, 216, 222, 227, 232, 237, 242

Offset: 1

Clark Kimberling

nonn

More terms and simpler title from Sean A. Irvine, Apr 06 2020

A030710 a(n)=least k such that s(k)=n, where s=A030707.

Original entry on oeis.org

1, 7, 3, 4, 16, 6, 29, 9, 38, 30, 14, 39, 20, 51, 84, 28, 152, 37, 82, 124, 83, 49, 177, 101, 64, 276, 123, 81, 146, 99, 173, 409, 357, 174, 121, 203, 314, 145, 237, 452, 238, 172, 562, 274, 202, 506, 312, 450, 313, 236, 687, 272, 686

Offset: 1

Clark Kimberling

nonn

A030712 Positions of records in A030707.

Original entry on oeis.org

1, 3, 4, 6, 9, 14, 20, 28, 37, 49, 64, 81, 99, 121, 145, 172, 202, 236, 272, 311, 353, 399, 447, 499, 556, 617, 682, 750, 821, 894, 971, 1052, 1136, 1224, 1316, 1411, 1510, 1615, 1723, 1834, 1948, 2067, 2191, 2317, 2447, 2583, 2725, 2872, 3022, 3177, 3335

Offset: 1

Clark Kimberling

nonn

Cf. A030711.

More terms and simpler title from Sean A. Irvine, Apr 06 2020

A030713 Numbers k such that A030707(k) = 1.

Original entry on oeis.org

1, 2, 5, 8, 10, 13, 19, 24, 27, 36, 43, 45, 48, 60, 63, 77, 80, 98, 113, 116, 117, 120, 141, 144, 163, 168, 171, 188, 201, 224, 231, 232, 235, 271, 306, 307, 310, 349, 352, 387, 394, 395, 398, 446, 478, 494, 495, 498, 538, 544, 551

Offset: 1

Clark Kimberling

nonn

A030714 Numbers k such that A030707(k) = 2.

Original entry on oeis.org

7, 12, 18, 26, 35, 47, 55, 57, 58, 62, 75, 79, 94, 97, 119, 135, 138, 139, 143, 170, 191, 196, 198, 200, 218, 234, 258, 265, 266, 268, 270, 309, 336, 346, 347, 351, 392, 397, 434, 441, 442, 445, 497, 530, 548, 549, 554, 595, 602

Offset: 1

Clark Kimberling

nonn

Cf. A030707.

A030715 Numbers k such that A030707(k) = 3.

Original entry on oeis.org

3, 11, 15, 17, 25, 32, 46, 61, 70, 72, 73, 78, 92, 96, 112, 118, 142, 159, 164, 166, 169, 199, 221, 227, 229, 233, 252, 269, 301, 302, 304, 308, 389, 390, 396, 430, 439, 490, 491, 496, 552, 587, 606, 607, 614, 662, 671, 673, 678

Offset: 1

Clark Kimberling

nonn

Cf. A030707.

A030716 Numbers k such that A030707(k) = 4.

Original entry on oeis.org

4, 23, 33, 34, 41, 59, 76, 89, 90, 115, 134, 162, 167, 194, 197, 230, 261, 263, 267, 294, 305, 341, 344, 348, 350, 378, 436, 437, 444, 483, 543, 545, 550, 610, 648, 656, 664, 669, 677, 727, 736, 738, 743, 792, 809, 816, 818, 883

Offset: 1

Clark Kimberling

nonn

Cf. A030707.

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

A030757 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 descending 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, 1, 4, 1, 2, 6, 1, 2, 3, 1, 8, 1, 2, 3, 5, 3, 11, 1, 2, 3, 1, 4, 8, 5, 13, 1, 2, 4, 4, 3, 6, 10, 7, 16, 1, 2, 3, 1, 5, 1, 6, 4, 9, 12, 9, 18, 1, 2, 3, 1, 4, 2, 2, 6, 2, 8, 6, 11, 14, 11, 22, 1, 2, 3, 1, 4, 2, 7, 3, 3, 8, 3, 11, 7, 13, 16, 16, 25, 1, 2, 3

Offset: 1

Clark Kimberling

nonn

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

The second list is A030758.

Cf. A030707, A030708, A030709.

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

cp's OEIS Frontend

A030709 Number of new terms at stage n in the formation of A030707.

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A030711 Record values in A030707.

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A030710 a(n)=least k such that s(k)=n, where s=A030707.

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A030712 Positions of records in A030707.

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A030713 Numbers k such that A030707(k) = 1.

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A030714 Numbers k such that A030707(k) = 2.

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A030715 Numbers k such that A030707(k) = 3.

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A030716 Numbers k such that A030707(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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A030757 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 descending order to the second list and add the corresponding frequencies of those values to the first list.

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