A390305 Numbers > 0 whose binary indices have strictly increasing first differences.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 22, 24, 32, 33, 34, 35, 36, 37, 38, 40, 44, 48, 64, 65, 66, 67, 68, 69, 70, 72, 74, 75, 76, 80, 88, 96, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 144, 148, 150, 152, 160, 176, 192, 256

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

Chris R. Rehmann, Table of n, a(n) for n = 1..10000

Chris R. Rehmann, Semilog plot

Example

The binary indices of 600 are (4,5,7,10), with first differences (1,2,3), so 600 is in the sequence.

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], Less@@Differences[bpe[#]]&]

Prog

(MATLAB) isA390305 = @(n) all(diff(diff(find(fliplr(dec2bin(n)-'0'))))>0); % Chris R. Rehmann, Dec 08 2025

Crossrefs

For prime indices we have A325456, counted by A240027.

The opposite for prime indices is A325457, counted by A320470.

For standard compositions see A333255, weak A225620.

The 0-prepended version is A333256.

Indicates strictly increasing rows of A390090.

The opposite version is A390306.

A011782 counts compositions.

A325545 counts compositions with distinct first differences.

A358133 lists first differences of standard compositions, row sums A358135.

Cf. A018900, A070211, A119387, A325546, A390091.

Cf. A000120, A029931, A048793, A070939, A124768.

Sequence in context: A277620 A031143 A358521 * A302594 A055492 A005459

Adjacent sequences: A390302 A390303 A390304 * A390306 A390307 A390308

Keyword

nonn,look

Author

Gus Wiseman, Nov 20 2025

Status

approved