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A343757 Irregular table read by rows; the n-th row contains the sums of distinct terms of the n-th row of table A343835, in ascending order. 2
0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 1, 4, 5, 0, 6, 0, 7, 0, 8, 0, 1, 8, 9, 0, 2, 8, 10, 0, 3, 8, 11, 0, 12, 0, 1, 12, 13, 0, 14, 0, 15, 0, 16, 0, 1, 16, 17, 0, 2, 16, 18, 0, 3, 16, 19, 0, 4, 16, 20, 0, 1, 4, 5, 16, 17, 20, 21, 0, 6, 16, 22, 0, 7, 16, 23, 0, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

In other words, the n-th row contains the numbers k whose runs of 1's in the binary expansion also appear in that of n.

The n-th row has 2^A069010(n) terms.

This sequence has similarities with A295989.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8120

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

Index entries for sequences related to binary expansion of n

FORMULA

T(n, 0) = 0.

T(n, 1) = A342410(n) for any n > 0.

T(n, 2^A069010(n)-1) = n.

EXAMPLE

Table begins:

0: [0]

1: [0, 1]

2: [0, 2]

3: [0, 3]

4: [0, 4]

5: [0, 1, 4, 5]

6: [0, 6]

7: [0, 7]

8: [0, 8]

9: [0, 1, 8, 9]

10: [0, 2, 8, 10]

11: [0, 3, 8, 11]

12: [0, 12]

13: [0, 1, 12, 13]

14: [0, 14]

15: [0, 15]

Table begins in binary:

0: [0]

1: [0, 1]

10: [0, 10]

11: [0, 11]

100: [0, 100]

101: [0, 1, 100, 101]

110: [0, 110]

111: [0, 111]

1000: [0, 1000]

1001: [0, 1, 1000, 1001]

1010: [0, 10, 1000, 1010]

1011: [0, 11, 1000, 1011]

1100: [0, 1100]

1101: [0, 1, 1100, 1101]

1110: [0, 1110]

1111: [0, 1111]

PROG

(PARI) row(n) = { my (rr=[]); while (n, my (z=valuation(n, 2), o=valuation(n/2^z+1, 2), r=(2^o-1)*2^z); n-=r; rr = concat(rr, r)); vector(2^#rr, k, vecsum(vecextract(rr, k-1))) }

CROSSREFS

Cf. A069010, A295989, A343835.

Sequence in context: A108416 A215395 A338569 * A108760 A343554 A137304

Adjacent sequences: A343754 A343755 A343756 * A343758 A343759 A343760

KEYWORD

nonn,base,tabf

AUTHOR

Rémy Sigrist, May 01 2021

STATUS

approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)