A090853 -id:A090853 - cp's OEIS frontend

A090852 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to n.

1, 4, 7, 10, 13, 16, 20, 24, 27, 31, 35, 39, 43, 47, 51, 55, 60, 64, 68, 73, 77, 81, 86, 90, 95, 100, 104, 109, 113, 118, 123, 127, 132, 137, 142, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 251, 256, 262

Offset: 1

Paul D. Hanna, Dec 10 2003

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Cf. A090853, A090854.

Table[Ceiling[y /. FindRoot[Pi/(2*EllipticK[1 - y^2]) == n, {y, 2*n}]], {n, 1, 60}] (* Vaclav Kotesovec, Sep 28 2019 *)

floor( agm(a(n), 1) ) = n, for n>=1.

A090854 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to Fibonacci(n).

Original entry on oeis.org

1, 1, 4, 7, 13, 24, 43, 77, 137, 241, 421, 732, 1266, 2178, 3733, 6376, 10858, 18439, 31237, 52804, 89082, 150014, 252206, 423367, 709697, 1188136, 1986730, 3318386, 5536857, 9229483, 15370775, 25576584, 42524547, 70649205, 117290710

Offset: 0

Paul D. Hanna, Dec 10 2003

nonn

Cf. A090852, A090853, A090855.

floor( agm(a(n), 1) ) = Fibonacci(n), for n>=0.

cp's OEIS Frontend

A090852 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to n.

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