A083951 Least increasing integer coefficients such that A(x)^(1/3) has only integer coefficients.

1, 3, 6, 7, 9, 12, 13, 15, 18, 21, 24, 27, 28, 30, 33, 34, 36, 39, 41, 42, 45, 47, 48, 51, 52, 54, 57, 60, 63, 66, 69, 72, 75, 77, 78, 81, 83, 84, 87, 88, 90, 93, 94, 96, 99, 100, 102, 105, 108, 111, 114, 116, 117, 120, 121, 123, 126, 127, 129, 132, 133, 135, 138, 139

Offset

0,2

Comments

a(k) == 1 (mod 3) at k=0,3,6,12,15,24,39,42,45,54,57,60,63,66,... a(k) == 2 (mod 3) at k=18,21,33,36,51,...

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..5000.

Mathematica

a[0] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Sum[ a[i]*x^i, {i, 0, n - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^n)^(1/3), {x, 0, n}], x]]] != True, k++ ]; k]; Array[ a, 70] (* Robert G. Wilson v, Sep 19 2008 *)

Crossrefs

Cf. A083349, A083953.

Sequence in context: A082847 A047242 A190335 * A284879 A208327 A131392

Adjacent sequences: A083948 A083949 A083950 * A083952 A083953 A083954

Keyword

nonn

Author

Paul D. Hanna, May 09 2003

Extensions

Three non-ascending values in the range 77 to 84 replaced with those from the b-file. - R. J. Mathar, Jan 14 2009

Status

approved