A394676 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) + a(k+3) is not term.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98

Offset

1,2

Comments

Conjecture 1: a(n) <= floor((5*n-1)/4).

Conjecture 2: The sequence L(k)=16^(k-1) + 3 describes the number of consecutive terms that match the formula a(n) = floor((5*n-1)/4): (Start)

[a(1)..a(4)] : L(1) = 16^(1-1) + 3 = 4

[a(22)..a(40)] : L(2) = 16^(2-1) + 3 = 19

[a(359)..a(617)] : L(3) = 16^(3-1) + 3 = 259

[a(5735)..a(9833)] : L(4) = 16^(4-1) + 3 = 4099

[a(91751)..a(157289)] : L(5) = 16^(5-1) + 3 = 65539

... (End).

Links

Table of n, a(n) for n=1..80.

Prog

(PARI)
a_seq(N) = {my(a = [1], used = Set([1]), forb = Set([]), maxv = 3); 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 >= 4, my(s = a[m-3] + a[m-2] + a[m-1] + a[m]); forb = setunion(forb, [s]); ); if(m >= 3, my(s = a[m-2] + a[m-1] + a[m] + (m+1 <= N)); ); if(m >= 1 && m+1 <= N && m+2 <= N && m+3 <= N, 0); ); a; };
A394676 = a_seq(1000);
vector(100, n, A394676[n])

Crossrefs

Cf. A047201.

Sequence in context: A069899 A081306 A130073 * A395790 A133812 A115661

Adjacent sequences: A394673 A394674 A394675 * A394677 A394678 A394679

Keyword

nonn

Author

Hoang Xuan Thanh, May 11 2026

Status

approved