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

Author

Paul D. Hanna, May 09 2003

Keywords

• nonn

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.

Crossrefs

Cf. A083349, A083953.

Programs

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 *)

Extensions

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