A363654 Lexicographically earliest sequence of positive integers such that the n-th pair of identical terms encloses exactly a(n) terms.

1, 2, 1, 3, 2, 3, 1, 2, 4, 3, 4, 5, 3, 6, 7, 4, 3, 8, 6, 9, 7, 8, 4, 10, 3, 7, 4, 6, 8, 9, 11, 10, 12, 3, 9, 13, 7, 3, 11, 9, 14, 15, 13, 16, 17, 7, 18, 3, 19, 20, 11, 14, 9, 20, 17, 15, 19, 20, 18, 21, 11, 22, 3, 23, 24, 25, 26, 14, 17, 9, 27, 28, 29, 15, 26, 19

Offset

1,2

Comments

Pairs are numbered according to the position of the second term.

Links

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

Eric Angelini, A seq with a strange behavior (or not)?

Neal Gersh Tolunsky, Scatterplot of first 100000 terms

Example

a(1) = 1. The 1st constructed pair encloses 1 term:  [1, 2, 1].
a(2) = 2. The 2nd constructed pair encloses 2 terms: [2, 1, 3, 2].
a(3) = 1. The 3rd constructed pair encloses 1 term:  [3, 2, 3].
a(4) = 3. The 4th constructed pair encloses 3 terms: [1, 3, 2, 3, 1].
a(5) = 2. The 5th constructed pair encloses 2 terms: [2, 3, 1, 2].
a(6) = 3. The 6th constructed pair encloses 3 terms: [3, 1, 2, 4, 3].
a(7) = 1. The 7th constructed pair encloses 1 term:  [4, 3, 4].
...

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    a, indexes = [1], {1: 0}
    yield a[-1]
    for i in count(0):
        num = 1
        while True:
            if num in indexes:
                if (len(a) - indexes[num]) == (a[i]+1):
                    an = num; indexes[an] = len(a); a.append(an); yield an
                    break
                else:
                    num += 1
            else:
                an = max(a)+1; indexes[an] = len(a); a.append(an); yield an
                num = 1
print(list(islice(agen(), 100))) # Gavin Lupo and Michael S. Branicky, Jun 13 2023

Crossrefs

Cf. A026272, A363708, A363757.

Sequence in context: A102853 A304099 A293390 * A189231 A107337 A066376

Adjacent sequences: A363651 A363652 A363653 * A363655 A363656 A363657

Keyword

nonn

Author

Eric Angelini and Gavin Lupo, Jun 13 2023

Status

approved