A361172 a(n) is the smallest positive number not among the terms between a(n-1) and the previous most recent occurrence of a(n-1) inclusive; if a(n-1) is a first occurrence, set a(n)=1; a(1)=1.

1, 1, 2, 1, 3, 1, 2, 4, 1, 3, 5, 1, 2, 6, 1, 3, 4, 7, 1, 2, 5, 8, 1, 3, 6, 9, 1, 2, 4, 10, 1, 3, 5, 7, 11, 1, 2, 6, 8, 12, 1, 3, 4, 9, 13, 1, 2, 5, 10, 14, 1, 3, 6, 7, 15, 1, 2, 4, 8, 11, 16, 1, 3, 5, 9, 12, 17, 1, 2, 6, 10, 13, 18, 1, 3, 4, 7, 14, 19, 1, 2, 5, 8, 15, 20, 1

Offset

1,3

Comments

The terms between two adjacent 1s must be strictly increasing.

The index of first occurrences appears to be A060432 (partial sums of A002024).

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Neal Gersh Tolunsky, Scatterplot of the first 13158 terms

Example

a(11)=5 because between a(10)=3 and the previous 3 (3, 1, 2, 4, 1, 3), the smallest missing number is 5, so a(11)=5.

Prog

(PARI) { pos = [0]; v = 1; for (n = 1, #a = vector(86), print1 (a[n] = v", "); v = 1; if (a[n] <= #pos && pos[a[n]], r = Set(a[pos[a[n]]..n]); while (setsearch(r, v), v++)); while (#pos < a[n], pos = concat(pos, vector(#pos)); ); pos[a[n]] = n; ); } \\ Rémy Sigrist, Mar 04 2023

Crossrefs

Cf. A060432, A358921, A361101.

Sequence in context: A057059 A368313 A346795 * A169896 A210208 A162306

Adjacent sequences: A361169 A361170 A361171 * A361173 A361174 A361175

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 02 2023

Status

approved