A384878 - OEIS

A384878

Position of first appearance of n in the flattened version of the triangle A384877, whose m-th row lists the lengths of maximal anti-runs in the binary indices of m.

1, 6, 34, 178, 882, 4210, 19570, 89202, 400498, 1776754

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OFFSET

1,2

COMMENTS

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

The set of binary indices of each nonnegative integer and its partition into anti-runs begins:

0: {} {{}}

1: {1} {{1}}

2: {2} {{2}}

3: {1,2} {{1},{2}}

4: {3} {{3}}

5: {1,3} {{1,3}}

6: {2,3} {{2},{3}}

7: {1,2,3} {{1},{2},{3}}

The flattened version begins: {}, {1}, {2}, {1}, {2}, {3}, {1,3}, {2}, {3}, {1}, {2}, {3}. Of these sets, the first of length 2 is the sixth (starting with 0), so we have a(2) = 6.

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];

q=Join@@Table[Length/@Split[bpe[n], #2!=#1+1&], {n, 0, 100}];

Table[Position[q, i][[1, 1]], {i, mnrm[q]}]

CROSSREFS

For runs instead of anti-runs we have A001792.

The unflattened version is A052499.

Positions of first appearances in A384877, see A000120, A245562, A245563, A384890.

A023758 lists differences of powers of 2.

A384175 counts subsets with all distinct lengths of maximal runs, complement A384176.

Cf. A044813, A048793, A069010, A384879, A384893.

Sequence in context: A344717 A266359 A198765 * A274405 A144142 A126643

Adjacent sequences: A384875 A384876 A384877 * A384879 A384880 A384881

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 23 2025

STATUS

approved