A356149 Irregular table T(n, k), n > 0, k = 1..A356148(n), read by rows; the n-th row contains, in ascending order, the distinct positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.

1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 6, 1, 3, 7, 1, 2, 3, 4, 7, 8, 1, 2, 3, 4, 6, 9, 1, 2, 5, 10, 1, 2, 3, 4, 5, 11, 1, 2, 3, 4, 6, 12, 1, 2, 3, 5, 6, 13, 1, 2, 3, 6, 7, 14, 1, 3, 7, 15, 1, 2, 3, 4, 7, 8, 15, 16, 1, 2, 3, 4, 6, 7, 8, 14, 17, 1, 2, 3, 4, 5, 6, 9, 13, 18

Offset

1,3

Comments

Leading 0's in binary expansions are ignored.

The n-th contains the n-th row of A165416.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..26775

Index entries for sequences related to binary expansion of n

Formula

T(n, 1) = 1.

T(n, A356148(n)) = n.

Example

Table T(n, k) begins:
    1;
    1, 2;
    1, 3;
    1, 2, 3, 4;
    1, 2, 5;
    1, 2, 3, 6;
    1, 3, 7;
    1, 2, 3, 4, 7, 8;
    1, 2, 3, 4, 6, 9;
    1, 2, 5, 10;
    1, 2, 3, 4, 5, 11;
    1, 2, 3, 4, 6, 12;
    1, 2, 3, 5, 6, 13;
    1, 2, 3, 6, 7, 14;
    1, 3, 7, 15;
    1, 2, 3, 4, 7, 8, 15, 16;
    ...

Prog

(PARI) row(n) = { my (b=binary(n)); setbinop((i, j) -> my (s=fromdigits(b[i..j], 2)); if (b[i], s, 2^(j-i+1)-1-s), [1..#b]) }
(Python)
def row(n):
    N = n.bit_length()
    c, s = ((1<<N)-1)^n, set()
    for i in range(N):
        for l in range(N-i):
            mask = ((2<<l)-1) << i
            s.add((mask&n) >> i)
            s.add((mask&c) >> i)
    return sorted(s - {0})
print([t for r in range(19) for t in row(r)]) # Michael S. Branicky, Jul 28 2022

Crossrefs

Cf. A165416, A356148, A356150.

Sequence in context: A277427 A231631 A280700 * A038566 A020652 A293248

Adjacent sequences: A356146 A356147 A356148 * A356150 A356151 A356152

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jul 28 2022

Status

approved