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

Author

Rémy Sigrist, Mar 30 2018

Keywords

• nonn
• base

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)).

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

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

Programs

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)))

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.