A301984 a(n) is the greatest positive number k such that the binary digits of any number in the interval 1..k appear in order but not necessarily as consecutive digits in the binary representation of n.

1, 2, 1, 2, 3, 3, 1, 2, 5, 6, 3, 4, 3, 3, 1, 2, 5, 6, 5, 6, 7, 7, 3, 4, 7, 7, 3, 4, 3, 3, 1, 2, 5, 6, 5, 6, 11, 11, 5, 6, 13, 14, 7, 8, 7, 7, 3, 4, 9, 10, 7, 8, 7, 7, 3, 4, 7, 7, 3, 4, 3, 3, 1, 2, 5, 6, 5, 6, 11, 11, 5, 6, 13, 14, 11, 12, 11, 11, 5, 6, 13, 14

Offset

1,2

Comments

Equivalently, a(n) is the greatest positive number k such that A301983(n, k) = k.

Apparently, the k-th record value is A089633(k), and the first term with this value has index A048678(A089633(k)).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Formula

a(n) <= A301977(n).

a(2*n) >= a(n).

a(2*n + 1) >= a(n) (with strict inequality if a(n) is even).

a(n) = 1 iff n is positive and belongs to A000225.

Example

The 13th row of A301983 is: 1, 2, 3, 5, 6, 7, 13; all numbers in the range 1..3 appear in this row, but the number 4 is missing; hence a(13) = 3.

Prog

(PARI) a(n) = my (b=binary(n), s=Set(1)); for (i=2, #b, s = setunion(s, Set(apply(v -> 2*v+b[i], s)))); for (u=1, oo, if (!setsearch(s, u), return (u-1)))

Crossrefs

Cf. A048678, A089633, A261461, A301977, A301983.

Sequence in context: A348330 A328471 A227909 * A210805 A303842 A057041

Adjacent sequences: A301981 A301982 A301983 * A301985 A301986 A301987

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2018

Status

approved