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A339674 Irregular triangle T(n, k), n, k >= 0, read by rows; for any number m with runs in binary expansion (r_1, ..., r_j), let R(m) = {r_1 + ... + r_j, r_2 + ... + r_j, ..., r_j}; row n corresponds to the numbers k such that R(k) is included in R(n), in ascending order. 1
0, 0, 1, 0, 1, 2, 3, 0, 3, 0, 3, 4, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 6, 7, 0, 7, 0, 7, 8, 15, 0, 1, 6, 7, 8, 9, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 3, 4, 7, 8, 11, 12, 15, 0, 3, 12, 15, 0, 1, 2, 3, 12, 13, 14, 15, 0, 1, 14, 15, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

For any m > 0, R(m) contains the partial sums of the m-th row of A227736; by convention, R(0) = {}.

The underlying idea is to take some or all of the rightmost runs of a number, and possibly merge some of them.

For any n >= 0, the n-th row:

- has 2^A000120(A003188(n)) terms,

- has first term 0 and last term A003817(n),

- has n at position A090079(n),

- corresponds to the distinct terms in n-th row of table A341840.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Rémy Sigrist, Scatterplot of (n, T(n, k)) for n <= 2^10

Rémy Sigrist, PARI program for A339674

Index entries for sequences related to binary expansion of n

FORMULA

T(n, 0) = 0.

T(n, A090079(n)) = n.

T(n, 2^A000120(A003188(n))-1) = A003817(n).

EXAMPLE

The triangle starts:

    0;

    0, 1;

    0, 1, 2, 3;

    0, 3;

    0, 3, 4, 7;

    0, 1, 2, 3, 4, 5, 6, 7;

    0, 1, 6, 7;

    0, 7;

    0, 7, 8, 15;

    0, 1, 6, 7, 8, 9, 14, 15;

    0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15;

    0, 3, 4, 7, 8, 11, 12, 15;

    0, 3, 12, 15;

    0, 1, 2, 3, 12, 13, 14, 15;

    0, 1, 14, 15;

    0, 15;

    ...

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000120, A003188, A003817, A090079, A227736, A341840.

Sequence in context: A059283 A160202 A195673 * A241070 A128621 A132385

Adjacent sequences:  A339671 A339672 A339673 * A339675 A339676 A339677

KEYWORD

nonn,base,tabf

AUTHOR

Rémy Sigrist, Feb 21 2021

STATUS

approved

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Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)