Revision History for A354906
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#7 by Michael De Vlieger at Fri Jun 24 17:19:49 EDT 2022
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#6 by Gus Wiseman at Thu Jun 23 23:49:55 EDT 2022
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#5 by Gus Wiseman at Thu Jun 23 23:49:14 EDT 2022
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| CROSSREFS
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Cf. `. A003242, `, A029837, A071625, A124767, A182857, A238279/A333755, A325278, A333381, A333489, A333629.
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#4 by Gus Wiseman at Thu Jun 23 21:32:03 EDT 2022
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| CROSSREFS
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For run-sums instead of run-lengths we have A246534 (first appearancesfirsts in A353849).
For runs instead of run-lengths we have A351015, (firsts ofin A351014.).
`A003242 counts anti-run compositions, ranked by A333489.
`A353744 ranks compositions with equal run-lengths, counted by A329738.
Cf. `~. `A003242, `A029837, A071625, A124767, ~`A182850, ~`, A182857, `~, A238279, ~`A323014/A333755, A325278, A333381, `A333629, A333489, A333755, ~`A353832, `A353848, ~`A353851A333629.
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#3 by Gus Wiseman at Thu Jun 23 14:43:30 EDT 2022
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| KEYWORD
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nonn,changed,more
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#2 by Gus Wiseman at Thu Jun 23 14:43:15 EDT 2022
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| NAME
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allocatedPosition of first appearance of n in A354579 = Number of distinct run-lengths forof Gusstandard Wisemancompositions.
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| DATA
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0, 1, 11, 119, 5615, 251871
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| OFFSET
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0,3
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| COMMENTS
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The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
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| EXAMPLE
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The terms together with their corresponding compositions begin:
0: ()
1: (1)
11: (2,1,1)
119: (1,1,2,1,1,1)
5615: (2,2,1,1,1,2,1,1,1,1)
251871: (1,1,1,2,2,1,1,1,1,2,1,1,1,1,1)
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| MATHEMATICA
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stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
pd=Table[Length[Union[Length/@Split[stc[n]]]], {n, 0, 10000}];
Table[Position[pd, n][[1, 1]]-1, {n, 0, Max@@pd}]
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| CROSSREFS
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The standard compositions used here are A066099, run-sums A353847/A353932.
The version for partitions is A006939, for run-sums A002110.
For run-sums instead of run-lengths we have A246534 (first appearances in A353849).
For runs instead of run-lengths we have A351015, firsts of A351014.
These are the positions of first appearances in A354579.
`A003242 counts anti-run compositions, ranked by A333489.
A005811 counts runs in binary expansion.
A333627 ranks the run-lengths of standard compositions.
A351596 ranks compositions with distinct run-lengths, counted by A329739.
`A353744 ranks compositions with equal run-lengths, counted by A329738.
A353852 ranks compositions with distinct run-sums, counted by A353850.
A353853-A353859 are sequences pertaining to composition run-sum trajectory.
A353860 counts collapsible compositions.
Cf. `~A029837, A071625, A124767, ~`A182850, ~`A182857, `~A238279, ~`A323014, A325278, A333381, `A333629, A333755, ~`A353832, `A353848, ~`A353851.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Gus Wiseman, Jun 23 2022
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| STATUS
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approved
editing
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#1 by Gus Wiseman at Sat Jun 11 11:24:14 EDT 2022
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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| STATUS
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approved
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