A376185
a(n) = denominator of the sum S(n) defined in A376062.
Original entry on oeis.org
12, 48, 624, 97968, 2399530224, 1439436326371902768, 517994234419759747473589427583418224, 67079506723028253472357256785558488997471406450171845011442457607246768
Offset: 1
The initial values of S(n) are 7/12, 43/48, 619/624, 97963/97968, 2399530219/2399530224, 1439436326371902763/1439436326371902768 ...
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.
A376244
Lexicographically earliest sequence of positive integers a(1), a(2), ... with the property that the lexicographically earliest sequence of positive integers b(1), b(2), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1 / (a(k)*b(k)) < 1, also implies that S(n) is never of the form (e_n - 1) / e_n for some integer e_n.
Original entry on oeis.org
3, 4, 5, 4, 7, 3, 9, 1, 11, 4, 13, 7, 9, 19, 10, 2, 23, 25, 29, 27, 53, 1, 17, 7, 2, 2, 15, 67, 22, 37
Offset: 1
The initial terms are:
n a(n) b(n) S(n)
- ---- ------ ---------------------------
1 3 1 1/3
2 4 1 7/12
3 5 1 47/60
4 4 2 109/120
5 7 2 823/840
6 3 17 4757/4760
7 9 177 7582661/7582680
8 1 399089 3026164178509/3026164178520
A376184
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)} is the sequence b(1)=5/4, b(2*i)=3/2, b(2*i+1)=6/5 (i>0).
Original entry on oeis.org
2, 5, 17, 341, 92753, 10753782821, 92515075960384748177, 10698799099944699918936107506299150093941, 91571441744782016867976366392607084634231243149599342901251284090792487979854033
Offset: 1
The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...
A376186
a(n) = denominator of the sum S(n) defined in A376184.
Original entry on oeis.org
8, 40, 680, 231880, 21507565640, 231287689900961870440, 21397598199889399837872215012598300187880, 228928604361955042169940915981517711585578107873998357253128210226981219949635080
Offset: 1
The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...
Cf.
A004168,
A082732,
A374663,
A375516,
A375531,
A375532,
A375781,
A375522,
A376048-
A376062,
A376184,
A376185.
Showing 1-5 of 5 results.
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