A376942 Irregular table read by rows: row(n) is the lexicographically earliest sequence of positive integers a(n,1), a(n,2), ... a(n,k) such that Sum_{m = n..(n+k-1)} 1/(m*a(n,m-n+1)) <= 1.

1, 1, 1, 2, 5, 100, 1, 1, 1, 1, 3, 53, 4947, 66072132, 1, 1, 1, 1, 1, 1, 23, 5270, 27999510, 1, 1, 1, 1, 1, 1, 1, 2, 4, 28, 8851, 1395426533, 3665346274452116372, 53925647181443925794153448868309082440, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 95, 54570, 3932969040, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 45, 2685, 8685204, 98388241169400

Offset

1,4

Comments

The terms in each row can grow rapidly in size, e.g., the 63rd and final term in row(25), 36333...86400, has 1728101 digits.

Conjecture: all rows have finite length.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..797

Scott R. Shannon, Unflattened table for n = 1..25.

Example

row(1) = 1 as 1/(1*1) = 1.
row(2) = 1, 1, 2, 5, 100 as 1/(2*1) + 1/(3*1) + 1/(4*2) + 1/(5*5) + 1/(6*100) = 1.
row(3) = 1, 1, 1, 1, 3, 53, 4947, 66072132 as 1/(3*1) + 1/(4*1) + 1/(5*1) + 1/(6*1) + 1/(7*3) + 1/(8*53) + 1/(9*4947) + 1/(10*66072132) = 1.
.
The table begins:
1;
1, 1, 2, 5, 100;
1, 1, 1, 1, 3, 53, 4947, 66072132;
1, 1, 1, 1, 1, 1, 23, 5270, 27999510;
1, 1, 1, 1, 1, 1, 1, 2, 4, 28, 8851, 1395426533, 3665346274452116372, 53925647181443925794153448868309082440;
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 95, 54570, 3932969040;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 45, 2685, 8685204, 98388241169400;
.
.
.
See the attached file for rows up to n = 25.

Crossrefs

Cf. A001008, A002805, A002387, A375781, A376056, A269993.

Sequence in context: A290871 A162569 A120800 * A277341 A066618 A027720

Adjacent sequences: A376939 A376940 A376941 * A376943 A376944 A376945

Keyword

nonn,tabf

Author

Scott R. Shannon, Oct 12 2024

Status

approved