A076538 -id:A076538 - cp's OEIS frontend

A367328 The x-coordinate of the point where x + y = n, x and y are integers and x/y is as close as possible to e.

0, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 37, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 48, 48, 49, 50

Offset: 1

Colin Linzer, Nov 14 2023

a(n) is nondecreasing; lim_{n->oo} a(n) = oo.

Swapping the x and y coordinate of the sequence does not yield the sequence defined as the point where x + y = n, x and y are integers and x/y is as close as possible to 1/e even when excluding terms that would lead to a division by 0.

			For n = 3, the possible points are (0,3), (1,2), (2,1) as any negative value would would be further from e than 0/3. The closest value to e out of these is 2/1 so a(3) = 2.

Cf. A001113 (e), A367329 (y-coordinate), A007676.

a(n) is always either ceiling(n*e/(1 + e)) or floor(n*e/(1 + e)) = A076538(n).

A370325 Decimal expansion of exp(1)/(1+exp(1)).

Original entry on oeis.org

7, 3, 1, 0, 5, 8, 5, 7, 8, 6, 3, 0, 0, 0, 4, 8, 7, 9, 2, 5, 1, 1, 5, 9, 2, 4, 1, 8, 2, 1, 8, 3, 6, 2, 7, 4, 3, 6, 5, 1, 4, 4, 6, 4, 0, 1, 6, 5, 0, 5, 6, 5, 1, 9, 2, 7, 6, 3, 6, 5, 9, 0, 7, 9, 1, 9, 0, 4, 0, 4, 5, 3, 0, 7, 0, 2, 0, 4, 6, 3, 9, 3, 8, 7, 4, 7, 4, 5, 3, 2, 0, 7, 5, 9, 8, 1

Offset: 0

R. J. Mathar, Feb 15 2024

			0.73105857863000487925115924182183627...

Index entries for transcendental numbers

Cf. A076538 (Beatty seq.), A001113, A201776, A068985.

Maple
```
exp(1)/(1+exp(1)) ; evalf(%) ;
```

RealDigits[E/(E + 1), 10, 120][[1]] (* Amiram Eldar, Feb 18 2024 *)

exp(1)/(exp(1)+1) \\ Amiram Eldar, Feb 18 2024

Equals A001113*A201776 = 1/(1 + A068985).

Equals 1/(1 + Sum_{k>=0} (-1)^k/k!). - Peter Luschny, Feb 15 2024

cp's OEIS Frontend

A367328 The x-coordinate of the point where x + y = n, x and y are integers and x/y is as close as possible to e.

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A370325 Decimal expansion of exp(1)/(1+exp(1)).

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