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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 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.)