

A301983


Irregular triangle read by rows T(n, k), n >= 1 and 1 <= k <= A301977(n): T(n, k) is the kth 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
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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^(k1) 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



