A379067 Smallest missing positive number after A377091(n) has been found.

1, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 14, 14, 14, 14, 14, 14, 14, 14, 15, 16, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 22, 22, 24, 24, 24, 24, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 51, 51, 51, 51, 51, 51, 51

Offset: 0

Author

N. J. A. Sloane, Dec 28 2024

Keywords

• nonn

Comments

Conjecture: lim sup |a(n) - n/2|/sqrt(n) = 1/2 (see links). This would imply that after A377091(n) has been found, A377091 contains all numbers in the range [0,f(n)], where lim sup f(n) = (n-sqrt(n))/2. There is a corresponding conjecture for A379068. - N. J. A. Sloane and Paolo Xausa, Feb 03 2025

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Table of n, A379067(n), A379068(n) for n = 0..999995.
• Paolo Xausa, Scatterplot of |a(n) - n/2|/sqrt(n) for 1 <= n <= 10^6. The orange line is y = 1/2.
• Paolo Xausa, Scatterplot of |a(n) - n/2|/sqrt(n) for 900000 <= n <= 10^6. The orange line is y = 1/2.

Crossrefs

Cf. A377091, A379068.

Programs

Mathematica

(* A377091list is defined at A377091 *)
Module[{s, a}, s[A377091list%5B100%5D%5D%5D%5D%20(*%20_Paolo%20Xausa">] := False; FoldList[(s[#2] = True; a = #; While[s[a], a++]; a) &, 1, Rest[A377091list[100]]]] (* _Paolo Xausa, Apr 08 2025 *)