A359051 Irregular table T(n, k), n > 0, k = 1..A000010(n); the n-th row lists the numbers k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487).

0, 1, 2, 3, 4, 7, 5, 6, 8, 15, 16, 31, 9, 11, 12, 14, 32, 63, 10, 13, 64, 127, 17, 23, 24, 30, 128, 255, 19, 28, 256, 511, 18, 20, 27, 29, 33, 47, 48, 62, 512, 1023, 22, 25, 1024, 2047, 21, 26, 35, 39, 56, 60, 65, 95, 96, 126, 2048, 4095, 34, 40, 55, 61, 4096, 8191

Offset

1,3

Comments

Every nonnegative integer m appears in this sequence (in row fusc(m) + fusc(m+1)).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..5022

Rémy Sigrist, PARI program

Index entries for sequences related to Stern's sequences

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 1) = A359050(n).

T(n, A000010(n)) = 2^(n-1) - 1.

Example

Array T(n, k) begins:
    0,
    1,
    2, 3,
    4, 7,
    5, 6, 8, 15,
    16, 31,
    9, 11, 12, 14, 32, 63,
    10, 13, 64, 127,
    17, 23, 24, 30, 128, 255,
    19, 28, 256, 511,
    18, 20, 27, 29, 33, 47, 48, 62, 512, 1023,
    22, 25, 1024, 2047,
    ...

Prog

(PARI) See Links section.

Crossrefs

Cf. A000010, A002487, A359050.

Sequence in context: A125978 A268131 A361646 * A014321 A175343 A239965

Adjacent sequences: A359048 A359049 A359050 * A359052 A359053 A359054

Keyword

nonn,tabf

Author

Rémy Sigrist, Dec 14 2022

Status

approved