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.

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

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