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

0,2

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.

Mathematica

(* A377091list is defined at A377091 *)
Module[{s, a}, s[_] := False; FoldList[(s[#2] = True; a = #; While[s[a], a++]; a) &, 1, Rest[A377091list[100]]]] (* Paolo Xausa, Apr 08 2025 *)

Crossrefs

Cf. A377091, A379068.

Sequence in context: A037458 A296816 A064474 * A072688 A381018 A120504

Adjacent sequences: A379064 A379065 A379066 * A379068 A379069 A379070

Keyword

nonn

Author

N. J. A. Sloane, Dec 28 2024

Status

approved