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

0,2

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.

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}]

Crossrefs

Cf. A083952, A134780.

Sequence in context: A132635 A182131 A298868 * A226250 A075325 A026278

Adjacent sequences: A134776 A134777 A134778 * A134780 A134781 A134782

Keyword

nonn

Author

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

Status

approved