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A301983 Irregular triangle read by rows T(n, k), n >= 1 and 1 <= k <= A301977(n): T(n, k) is the k-th positive number whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n. 3
1, 1, 2, 1, 3, 1, 2, 4, 1, 2, 3, 5, 1, 2, 3, 6, 1, 3, 7, 1, 2, 4, 8, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 5, 6, 10, 1, 2, 3, 5, 7, 11, 1, 2, 3, 4, 6, 12, 1, 2, 3, 5, 6, 7, 13, 1, 2, 3, 6, 7, 14, 1, 3, 7, 15, 1, 2, 4, 8, 16, 1, 2, 3, 4, 5, 8, 9, 17, 1, 2, 3, 4, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence has similarities with A119709 and A165416; there we consider consecutive digits, here not.

LINKS

Rémy Sigrist, Rows n = 1..500 of triangle, flattened

Index entries for sequences related to binary expansion of n

FORMULA

T(n, 1) = 1.

T(n, A301977(n)) = n.

T(2^n, k) = 2^(k-1) for any n > 0 and k = 1..n+1.

T(2^n - 1, k) = 2^k - 1 for any n > 0 and k = 1..n.

EXAMPLE

Triangle begins:

   1:    [1]

   2:    [1, 2]

   3:    [1, 3]

   4:    [1, 2, 4]

   5:    [1, 2, 3, 5]

   6:    [1, 2, 3, 6]

   7:    [1, 3, 7]

   8:    [1, 2, 4, 8]

   9:    [1, 2, 3, 4, 5, 9]

  10:    [1, 2, 3, 4, 5, 6, 10]

  11:    [1, 2, 3, 5, 7, 11]

  12:    [1, 2, 3, 4, 6, 12]

  13:    [1, 2, 3, 5, 6, 7, 13]

  14:    [1, 2, 3, 6, 7, 14]

  15:    [1, 3, 7, 15]

  16:    [1, 2, 4, 8, 16]

PROG

(PARI) T(n, k) = my (b=binary(n), s=Set(1)); for (i=2, #b, s = setunion(s, Set(apply(v -> 2*v+b[i], s)))); return (s[k])

CROSSREFS

Cf. A119709, A165416, A301977 (row length).

Sequence in context: A228812 A144113 A304038 * A165416 A222818 A057059

Adjacent sequences:  A301980 A301981 A301982 * A301984 A301985 A301986

KEYWORD

nonn,base,tabf

AUTHOR

Rémy Sigrist, Mar 30 2018

STATUS

approved

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Last modified December 11 02:29 EST 2019. Contains 329911 sequences. (Running on oeis4.)