A353985 -id:A353985 - cp's OEIS frontend

A353983 Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a Catalan number (A000108).

3, 4, 6, 9, 12, 13, 28, 31, 34, 59, 62, 65, 90, 145, 297, 328, 673, 1001, 1298, 2134, 3432, 4433, 7501, 11934, 15366, 26624, 41990, 53924, 95302, 149226, 191216, 343672, 534888, 684114, 1247426, 1931540, 2466428, 4553977, 7020405, 8951945, 16710880, 25662825

Offset: 1

Rémy Sigrist, May 13 2022

nonn

The sequence is well defined:
- a(1) = 3,
- for n > 0, let k be such that A000108(k) + 1 + a(1) + ... + a(n) < A000108(k+1),
- then a(n+1) <= A000108(k) + 1.

Rémy Sigrist, C++ program

See A353889 for similar sequences.

Cf. A000108, A353984, A353985.

A353984 a(n) is the number of ways to write n as a sum of distinct terms of A353983.

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 3, 0, 2, 3, 1, 2, 3, 1, 2, 4, 1, 1, 4, 2, 1, 4, 2, 1, 5, 3, 0, 6, 4, 0, 5, 5, 0, 6, 6, 0, 7, 8, 1, 6, 10, 2, 6, 10, 3, 5, 11, 4, 4, 11, 5, 3, 12, 6, 2, 13, 8, 1, 13, 10, 0, 13, 11, 0, 13, 14, 0, 14, 17, 2, 13, 20, 4, 12

Offset: 0

Rémy Sigrist, May 14 2022

nonn

a(0) = 1 accounts for the empty sum.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, Scatterplot of the first 16796 terms
Rémy Sigrist, C++ program

Cf. A353983, A353985 (positions of 0's).

cp's OEIS Frontend

A353983 Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a Catalan number (A000108).

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