A134779 Integer coefficients of A(x), where a(n) is the least integer greater than a(n-1)+2 such that A(x)^(1/2) has integer coefficients.

1, 4, 6, 8, 11, 14, 16, 18, 21, 24, 27, 30, 33, 36, 38, 40, 43, 46, 49, 52, 55, 58, 61, 64, 66, 68, 71, 74, 76, 78, 80, 82, 85, 88, 90, 92, 95, 98, 101, 104, 106, 108, 111, 114, 117, 120, 122, 124, 126, 128, 131, 134, 137, 140, 143, 146, 148, 150, 153, 156, 159, 162, 164

Offset: 0

Author

Paul D. Hanna & Robert G. Wilson v, Nov 04 2007; definition corrected Sep 19 2008

Keywords

• nonn

Comments

If the condition for a(n) is simply to be greater than a(n-1) then the sequence is A000027: the natural numbers.

a(n)~5/2*n.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..7012.

Crossrefs

Cf. A083952, A134780.

Programs

Mathematica

a[n_] := a[n] = Block[{k = a[n - 1] + 2, s = Sum[ a[i]*x^i, {i, 0, n - 1}]}, While[ !IntegerQ@ Last@ CoefficientList[ Series[ Sqrt[s + k*x^n], {x, 0, n}], x], k++ ]; k]; a[0] = 1; Table[ a[n], {n, 0, 63}]