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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A003662 A132635 A182131 * 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

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Last modified December 18 19:05 EST 2014. Contains 252174 sequences.