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A030718 The second 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. 2

%I #19 Nov 19 2022 08:56:42

%S 1,1,1,2,1,2,1,2,3,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,

%T 1,2,3,4,5,6,7,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,11,1,2,3,4,5,6,7,8,9,

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

%N The second 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.

%H Seiichi Manyama, <a href="/A030718/b030718.txt">Table of n, a(n) for n = 1..10000</a>

%e Second list begins:

%e 1;

%e 1;

%e 1, 2;

%e 1, 2;

%e 1, 2, 3;

%e 1, 2, 3;

%e 1, 2, 3, 4;

%e 1, 2, 3, 4, 5;

%e 1, 2, 3, 4, 5, 6;

%e 1, 2, 3, 4, 5, 6, 7;

%e 1, 2, 3, 4, 5, 6, 7;

%e 1, 2, 3, 4, 5, 6, 7, 8;

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 11;

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15;

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18;

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

%t s = t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]]; AppendTo[s, Union@ Flatten@ t], {12}]; Flatten[s] (* _Michael De Vlieger_, Nov 15 2022, after _Peter J. C. Moses_ at A030717 *)

%Y Cf. A030717 (1st list).

%K nonn

%O 1,4

%A _Clark Kimberling_

%E Name revised in line with A030778 by _Peter Munn_, Oct 11 2022

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)