A269023 -id:A269023 - cp's OEIS frontend

A269020 a(n) = ceiling(n^(1+1/n)).

1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 1

Bob Selcoe, Feb 17 2016

			a(5)=7 because 5^(6/5) ~ 6.8986; a(6)=9 because 6^(7/6) ~ 8.088.

Cf. A059921 (floor(n^(1+1/n))), A269023 (complementary sequence).

[Ceiling(n^(1+1/n)): n in [1..70]]; // Vincenzo Librandi, Feb 18 2016

Table[Ceiling[n^(1 + 1 / n)], {n, 100}] (* Vincenzo Librandi, Feb 18 2016 *)

from sympy import integer_nthroot
def A269020(n):
    a, b = integer_nthroot(n**(n+1),n)
    return a+(b^1) # Chai Wah Wu, Sep 04 2024

a(n) = A059921(n) + 1, n>=2.

A269024 a(n) = A269020(n) - n.

Original entry on oeis.org

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Bob Selcoe, Feb 18 2016

nonn

Same as subtracting the index (n) from the output (a(n)) in A269020.

			a(20)=4 because A269020(20) = 24, and 24-20=4.
a(5)=2, a(6)=3 and A269023(3)=8, so a(6) = 8-6+1 = 3.

Cf. A269020, A269023.

a(n) = either a(n-1) or a(n-1)+1.

When a(n) = a(n-1)+1, a(n) = A269023(a(n)) - n + 1.

cp's OEIS Frontend

A269020 a(n) = ceiling(n^(1+1/n)).

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