Sylvia Zevi Abrams - cp's OEIS frontend

User: Sylvia Zevi Abrams

Sylvia Zevi Abrams's wiki page.

Sylvia Zevi Abrams has authored 2 sequences.

A361669 a(n) = floor of sinh(sinh(sinh(...(1)...))) with n iterations.

Original entry on oeis.org

1, 1, 1, 2, 3, 22, 3355531547

Offset: 0

Sylvia Zevi Abrams, Mar 20 2023

a(7) = ~2.67*10^1457288834.

sinh(x) = (e^x - e^-x)/2 is dominated by e^x as x tends to infinity, meaning that the sequence grows tetrationally.

			a(0) = 1,
a(1) = floor(sinh(1)) = floor(1.175...) = 1,
a(2) = floor(sinh(sinh(1))) = floor(1.465...) = 1,
a(3) = floor(sinh(sinh(sinh(1)))) = floor(2.048...) = 2,
a(4) = floor(sinh(sinh(sinh(sinh(1))))) = floor(3.812...) = 3,
a(5) = floor(sinh(sinh(sinh(sinh(sinh(1)))))) = floor(22.627...) = 22,
a(6) = floor(sinh(sinh(sinh(sinh(sinh(sinh(1))))))) = 3355531547.

Eric Weisstein's World of Mathematics, Hyperbolic Sine.

Cf. A000471, A073742.

a:= n-> floor(evalf((sinh@@n)(1), 45)):
seq(a(n), n=0..6);  # Alois P. Heinz, Mar 20 2023

Mathematica
```
Table[Floor[Nest[Sinh[n],1,n]],{n,0,7}]
```

A355617 a(1) = 1; a(2) = 2; for n > 2, a(n) = R(a(n-1)) if a(n-1) != R(a(n-2)) and R(a(n-1)) has not yet been used, where R is the digit reversal function A004086, otherwise a(n) is the smallest positive integer > a(n-1) that has not yet been used.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 101, 102, 201, 202, 203, 302, 303, 304, 403, 404, 405, 504, 505, 506, 605, 606, 607, 706, 707, 708, 807, 808, 809, 908, 909

Offset: 1

Sylvia Zevi Abrams, Jul 09 2022

A regular pattern of rectangles, each 10 times larger than the last, appears on the scatter plot of this sequence. However, there are moments where the sequence deviates from its current rectangle to drop down to lower orders of magnitude or jump up to higher ones. Additionally, chaotic behavior can be observed at values of n in the approximate intervals [60000, 63000], [68000, 82000], and [85000, 100000].

Not all integers appear in this sequence. The smallest number that will never occur is 130, as the only way to achieve the number is through 129, which had already been used to jump to 921.

			a(11) = 11 because R(a(10)) = 1, which was already used as a(1).
a(13) = 21 because R(a(12)) = 21, which had not yet been used, and a(11) =! R(a(12)).
a(64) = 20 because although R(a(63)) = 91 and 91 has not yet been used, a(63) = R(a(62)).

Sylvia Zevi Abrams, Table of n, a(n) for n = 1..10000 [Corrected to remove leading 0's by _Sean A. Irvine_]
Sylvia Zevi Abrams, Scatter Plot, for n < 100000

Cf. A004086.

R(n) = fromdigits(Vecrev(digits(n))); \\ A004086
leastunused(va, m) = my(k=va[m]+1); while (#select(x->(x==k), va), k++); k;
lista(nn) = my(va = vector(nn)); va[1] = 1; va[2] = 2; for (n=3, nn, if ((va[n-1] != R(va[n-2])) && !#select(x->(x==R(va[n-1])), va), va[n] = R(va[n-1]), va[n] = leastunused(va, n-1));); va; \\ Michel Marcus, Jul 12 2022

cp's OEIS Frontend

User: Sylvia Zevi Abrams

A361669 a(n) = floor of sinh(sinh(sinh(...(1)...))) with n iterations.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica