A376057
a(n) is the denominator of the sum S(n) defined in A376056.
Original entry on oeis.org
1, 2, 14, 994, 6917246, 430634636937890, 2039908095836912108987531110990, 54095925512992695768212345567905438957243461489279855615252290
Offset: 0
The first few values of S(n) are 0/1, 1/2, 13/14, 993/994, 6917245/6917246, 430634636937889/430634636937890, ...
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a:= proc(n) a(n):= `if`(n=0, 1, ((2*n-1)*a(n-1)+1)*a(n-1)) end:
seq(a(n), n=0..7); # Alois P. Heinz, Oct 18 2024
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RecurrenceTable[{a[n+1] == (2*n+1)*a[n]^2 + a[n], a[0] == 1}, a, {n, 0, 7}] (* Amiram Eldar, Sep 15 2024 *)
A376048
Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} = 3,1,4,1,5,... are the digits of Pi (cf. A000796).
Original entry on oeis.org
4, 5, 81, 1621, 13130101, 310319170452181, 21399552788917656689963823241, 1373822578697020375503379392874191898311737749943783762521
Offset: 1
- Rémy Sigrist and N. J. A. Sloane, Dampening Down a Divergent Series, Manuscript in preparation, September 2024.
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.
Original entry on oeis.org
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
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.
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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;
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.
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See the attached file for rows up to n = 25.
Showing 1-3 of 3 results.
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