A331910 -id:A331910 - cp's OEIS frontend

A332864 Lexicographically earliest sequence of positive integers with the property that the distance between the first appearance of n and the first appearance of n+1 is a(n).

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

Offset: 1

Samuel B. Reid, Feb 27 2020

nonn

Samuel B. Reid, Table of n, a(n) for n = 1..10000
Samuel B. Reid, C program for A332864
Samuel B. Reid, Graph of 10000 terms

Cf. A309681, A331910.

C
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See Links section.
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a = [1]
for n in range(1, 30):
    a += [1] * (a[n-1]-1)
    a.append(n+1)
print(a)
# Andrey Zabolotskiy, Feb 28 2020

A381894 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum.

Original entry on oeis.org

1, 2, 2, 1, 1, 3, 5, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 3, 3, 3, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 11, 11, 11, 13, 13, 13, 15, 15, 15, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9

Offset: 1

Neal Gersh Tolunsky, Mar 09 2025

nonn

			a(6) = 3 because the 4th run must have length a(4) = 1, and the potential runs 1 and 2 have the same sum as a run already in the sequence (namely 1 and 1,1). So a(6) = 3 since no run has appeared with a sum of 3 thus far.

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

Cf. A331910, A382028, A000002.

A382028 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same product.

Original entry on oeis.org

1, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 4, 4, 4, 5, 5, 5, 6, 6, 6, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5

Offset: 1

Neal Gersh Tolunsky, Mar 12 2025

nonn

			a(12)..a(13) = 4: This is the 6th run. a(6) = 2, so the 6th run has length 2. We cannot use 1 as any run of 1s would have the same product as the first run a(1) = 1. Runs of length 2 made of 2s and 3s have already occurred, so a(12)..a(13) = 4.
a(27)..a(30) = 3: This is the 12th run. a(12) = 4, so the 12th run has length 4. We cannot use 1 for the same reason mentioned above. We cannot have 2 because a run of four 2s has product 16, which would be the same as that of the 6th run of two 4s. So a(27)..a(30) = 3, a run whose product has not occurred before in a previous run.

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

Cf. A331910, A381894, A000002.

cp's OEIS Frontend

A332864 Lexicographically earliest sequence of positive integers with the property that the distance between the first appearance of n and the first appearance of n+1 is a(n).

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A381894 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum.

Views

Author

Keywords

Examples

Links

Crossrefs

A382028 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same product.

Views

Author

Keywords

Examples

Links

Crossrefs