A358424 -id:A358424 - cp's OEIS frontend

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.

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

A358423 Numbers k such that A030717(k) = 5.

Original entry on oeis.org

16, 18, 68, 76, 80, 89, 90, 93, 105, 109, 123, 143, 168, 286, 322, 366, 405, 448, 493, 494, 540, 541, 543, 591, 593, 646, 702, 770, 826, 832, 891, 893, 897, 960, 962, 966, 1032, 1034, 1039, 1110, 1112, 1117, 1193, 1195, 1200, 1279, 1281, 1286, 1367, 1369, 1374, 1459, 1461, 1466, 1554, 1556

Offset: 1

Seiichi Manyama, Nov 15 2022

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..8044 (first 1000 term by Seiichi Manyama)
Michael De Vlieger, Plot a(s(j) + k - 1) at (j,k) for j = 1..512 and s = partial sums of A030719, showing a(m) = 5 in red, a(m) = 1 in medium blue for reference, and other values of a(m) in light blue

Cf. A030723, A030724, A030725, A030726, A358424, A358425.

Cf. A030717.

t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {44}]; Position[DeleteCases[Flatten[t], 0], 5][[All, 1]] (* Michael De Vlieger, Nov 15 2022, after Peter J. C. Moses at A030717 *)

A358425 Numbers k such that A030717(k) = 7.

Original entry on oeis.org

25, 29, 31, 193, 250, 323, 361, 401, 402, 445, 490, 537, 587, 640, 696, 701, 756, 761, 818, 823, 883, 888, 952, 957, 1024, 1029, 1102, 1107, 1185, 1190, 1271, 1276, 1359, 1364, 1451, 1456, 1546, 1551, 1645, 1650, 1750, 1755, 1860, 1865, 1974, 1979, 2091, 2096, 2213, 2218, 2338

Offset: 1

Seiichi Manyama, Nov 15 2022

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..4046
Michael De Vlieger, Plot a(s(j) + k - 1) at (j,k) for j = 1..512 and s = partial sums of A030719, showing a(m) = 7 in red, a(m) = 1 in medium blue for reference, and other values of a(m) in light blue.

Cf. A030723, A030724, A030725, A030726, A358423, A358424.

Cf. A030717.

nn = 50; m = 7; c[] = 0; k = a[1] = c[1] = 1; Reap[Do[w = Union@ Array[a, k]; Do[Set[a[j + k], c[w[[j]]]]; If[a[j + k] == m, Sow[m]], {j, Length[w]}]; Do[c[a[j + k]]++, {j, Length[w]}]; k += Length[w], {n, nn}] ][[-1, -1]] (* _Michael De Vlieger, Nov 19 2022 *)

A358479 Number of 6's that appeared in the n-th step when constructing A030717.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Seiichi Manyama, Nov 18 2022

nonn

Also first differences of A358474.

Cf. A358467, A358469, A358476, A358477, A358478, A358480.

Cf. A030717, A358424.

cp's OEIS Frontend

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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A358423 Numbers k such that A030717(k) = 5.

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A358425 Numbers k such that A030717(k) = 7.

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A358479 Number of 6's that appeared in the n-th step when constructing A030717.

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