A219661 -id:A219661 - cp's OEIS frontend

A230416 The infinite trunk of factorial beanstalk (A219666) with reversed subsections.

0, 1, 5, 2, 23, 17, 12, 10, 7, 119, 109, 102, 97, 92, 85, 79, 74, 70, 63, 57, 52, 48, 46, 40, 35, 30, 28, 25, 719, 704, 693, 680, 670, 658, 648, 641, 630, 623, 612, 605, 597, 584, 574, 562, 552, 545, 534, 527, 516, 509, 501, 492, 486, 481, 476, 465, 455, 443

Offset: 0

Antti Karttunen, Oct 22 2013

Can be viewed also as an irregular table: after the initial zero on row 0, start each row n with (n!)-1 and subtract repeatedly the sum of factorial expansion digits (A034968) to get successive terms, until the number that has already been listed [which is always (n-1)!-1] is encountered, which is not listed second time, but instead, the current row is finished and the next row starts with ((n+1)!-1), with the same process repeated.

Contains the terms in the infinite trunk of factorial beanstalk (A219666) listed in partially reversed manner: after the initial zero each subsequence lists A219661(n) successive terms from A219666, descending from (n!)-1 downwards.

			This irregular table begins as:
0;
1;
5, 2;
23, 17, 12, 10, 7;
119, 109, 102, 97, 92, 85, 79, 74, 70, 63, 57, 52, 48, 46, 40, 35, 30, 28, 25;
...
After the initial zero (on row 0), each row n is A219661(n) elements long.

Antti Karttunen, Rows 0..7, flattened

Cf. A219666, A219661, A000142, A219651.
The rows are the initial portions of every (n!-1)th row in A219659.
Analogous sequence for binary system: A218616.

For n < 3, a(n) = (n+1)!-1, and for n >= 3, a(n) = (k+2)!-1 if A219651(a(n-1)) is of form k!-1, otherwise just A219651(a(n-1)).

a(n) = A219666(A230432(n)). [Consequence of the definitions]

A230411 a(n) = minimal k for which A219665(k) >= n; a(n) = one more than the factorial base width (A084558) of the (n-1)th term in the infinite trunk of factorial beanstalk (A219666).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 22 2013

nonn

a(1)=1, after which each term n occurs A219661(n-1) times.

Auxiliary function for computing A219666, A230431 and A230432.

Antti Karttunen, Table of n, a(n) for n = 1..5000

Cf. A219661, A219665, A219666, A230431, A230432.

Analogous sequence for binary system: A213711.

a(n) = 1 + A084558(A219666(n-1)) = 1 + A084558(A230416(n-1)). [Each a(n) is one more than the number of digits needed in factorial base to write the (n-1)-th term in the infinite trunk of factorial beanstalk]

A230421 Triangle A230420 transposed.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 4, 4, 5, 6, 12, 14, 16, 19, 22, 55, 59, 65, 73, 82, 94, 293, 314, 336, 362, 395, 432, 479, 1881, 1971, 2073, 2189, 2324, 2482, 2667, 2886, 14011, 14555, 15140, 15775, 16473, 17249, 18124, 19123, 20276, 115974, 120010, 124289, 128831, 133664, 138828, 144378, 150389, 156961, 164224

Offset: 1

Antti Karttunen, Oct 18 2013

			The first rows of this triangular table are:
1;
1, 1;
1, 2, 2;
4, 4, 5, 6;
12, 14, 16, 19, 22;
55, 59, 65, 73, 82, 94;
...

Transpose: A230420. Row sums: A219661.

(define (A230421 n) (A230420 (A038722 n)))

a(n) = A230420(A038722(n)).

cp's OEIS Frontend

A230416 The infinite trunk of factorial beanstalk (A219666) with reversed subsections.

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A230411 a(n) = minimal k for which A219665(k) >= n; a(n) = one more than the factorial base width (A084558) of the (n-1)th term in the infinite trunk of factorial beanstalk (A219666).

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A230421 Triangle A230420 transposed.

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