

A343757


Irregular table read by rows; the nth row contains the sums of distinct terms of the nth 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
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OFFSET

0,5


COMMENTS

In other words, the nth row contains the numbers k whose runs of 1's in the binary expansion also appear in that of n.
The nth 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^o1)*2^z); n=r; rr = concat(rr, r)); vector(2^#rr, k, vecsum(vecextract(rr, k1))) }


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



