A090856 -id:A090856 - cp's OEIS frontend

A090855 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 2^n.

1, 4, 10, 24, 55, 127, 288, 640, 1408, 3069, 6642, 14281, 30544, 65028, 137896, 291399, 613885, 1289715, 2702909, 5652038, 11795170, 24570079, 51095155, 106092067, 219972452, 455493427, 942031726, 1946056082, 4015916211

Offset: 0

Paul D. Hanna, Dec 10 2003

nonn

Cf. A090852, A090854, A090856.

Flatten[{1, Table[Ceiling[y /. FindRoot[Log[Pi/(2*EllipticK[1 - y^2])] == n*Log[2], {y, n*2^n}, MaxIterations -> 1000]], {n, 1, 50}]}] (* Vaclav Kotesovec, Sep 28 2019 *)

floor( agm(a(n), 1) ) = 2^n, for n>=0.

A090857 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 2^n is equal to 3^n.

Original entry on oeis.org

1, 5, 17, 59, 203, 690, 2308, 7621, 24913, 80794, 260303, 834057, 2660049, 8449715, 26747224, 84407894, 265647824, 834016199, 2612728134, 8168761695, 25494031748, 79434416090, 247130166428, 767788267178, 2382328079245

Offset: 0

Paul D. Hanna, Dec 10 2003

nonn

			a(6)=2308 since floor(agm(2308,2^6))=729=3^6, but floor(agm(2307,2^6))=728.

Cf. A090852, A090855, A090856.

floor( agm(a(n), 2^n) ) = 3^n, for n>=0.

cp's OEIS Frontend

A090855 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 2^n.

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