A348243 -id:A348243 - cp's OEIS frontend

A348444 If A348243(n) = i, then a(n) = 1 + number of copies of i that have already appeared in A348243.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 1

N. J. A. Sloane, Oct 21 2021

nonn

In other words, when we see i in A348243, which i is it? The first, second, third, ...? This gives a measure of how many attempts we have to make in A307730 and A349243 before all the n instances of n have been obtained.
The first 3's appear at n = 259, 490, 585, 627, ..., the first 4's at 3161, 4230, 5989, 8207, ...
Note that A348409 gives the index of the last occurrence of each k in A307730. So until we reach A348409(k), we will not know how many attempts are needed to obtain all copies of k.

N. J. A. Sloane, Table of n, a(n) for n = 1..750

Cf. A307720, A307730, A348245, A348409.

A348245 If A307730(n) = i, then a(n) = 1 + number of copies of i that have already appeared in A307730.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 4, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 1

N. J. A. Sloane, Oct 16 2021

nonn

From the definition of A307720 and A307730, we know that any number i must eventually appear exactly i times in A307730. So a(n) <= A307730(n).

N. J. A. Sloane, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Table of n, a(n) for n = 1..999999

Cf. A307720, A307730, A348243.

A348444 is another version.

A348395 Terms in A307730 in order of appearance.

Original entry on oeis.org

1, 2, 3, 6, 4, 9, 12, 8, 15, 5, 7, 14, 10, 21, 18, 24, 16, 27, 36, 20, 28, 32, 45, 25, 30, 35, 42, 49, 56, 40, 48, 63, 54, 72, 64, 81, 90, 50, 60, 70, 80, 99, 11, 13, 26, 22, 39, 33, 44, 55, 65, 52, 78, 66, 91, 77, 88, 110, 100, 121, 132, 84, 96, 108, 120, 143

Offset: 1

Rémy Sigrist, Oct 17 2021

nonn

Equivalently, terms in A348243 in order of appearance.

			Sequence A307730 starts: 1, 2, 2, 3, 3, 3, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 9.
So the present sequence starts: 1, 2, 3, 6, 4, 9.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A348395

Cf. A307720, A307730, A348243.

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cp's OEIS Frontend

A348444 If A348243(n) = i, then a(n) = 1 + number of copies of i that have already appeared in A348243.

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A348245 If A307730(n) = i, then a(n) = 1 + number of copies of i that have already appeared in A307730.

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A348395 Terms in A307730 in order of appearance.

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