A394576 a(1) = 1; a(n+1) as the smallest positive integer greater than a(n) that avoids violating the condition a(k) + a(k+1) + a(k+2) is not term.

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 99

Offset

1,2

Comments

Conjecture 1: a(n) <= floor((4*n-1)/3).

Conjecture 2: The sequence L(k) = 9^(k-1) + 2 describes the number of consecutive terms that match the formula a(n) = floor((4*n-1)/3) : (Start)

[a(1)..a(3)] : L(1) = 9^(1-1) + 2 = 3

[a(8)..a(18)] : L(2) = 9^(2-1) + 2 = 11

[a(71)..a(153)] : L(3) = 9^(3-1) + 2 = 83

[a(908)..a(1638)] : L(4) = 9^(4-1) + 2 = 731

[a(5741)..a(12303)] : L(5) = 9^(5-1) + 2 = 6563

[a(51668)..a(110718)] : L(6) = 9^(6-1) + 2 = 59051

[a(465011)..a(996453)] : L(7) = 9^(7-1) + 2 = 531443

... (End).

Links

Table of n, a(n) for n=1..75.

Prog

(PARI)
a_seq(N) = {my(a = [1], used = Set([1]), forb = Set([]), maxv = 2); while(#a < N, my(cand = a[#a] + 1); while(1, if( setsearch(used, cand)==0 && setsearch(forb, cand)==0, break); cand++; ); a = concat(a, cand); used = setunion(used, [cand]); my(m = #a); if(m >= 3, my(s = a[m-2] + a[m-1] + a[m]); forb = setunion(forb, [s]); ); if(m >= 2, my(s = a[m-1] + a[m] + (m+1 <= N)); ); if(m >= 1 && m+1 <= N && m+2 <= N, 0); ); a; };
A394576 = a_seq(1000);
vector(100, n, A394576[n]) \\ Hoang Xuan Thanh, May 14 2026

Crossrefs

Cf. A042968.

Sequence in context: A228803 A037014 A261131 * A225061 A133223 A065003

Adjacent sequences: A394573 A394574 A394575 * A394577 A394578 A394579

Keyword

nonn

Author

Hoang Xuan Thanh, May 11 2026

Status

approved