A108783 Positions of 1's in A083952, where A083952 gives the integer coefficients a(n) of A(x), where a(n) = 1 or 2 for all n, such that A(x)^(1/2) has only integer coefficients.

0, 2, 6, 10, 12, 26, 30, 32, 36, 50, 52, 56, 60, 62, 126, 130, 132, 136, 150, 152, 160, 164, 166, 170, 172, 174, 176, 180, 184, 192, 194, 198, 200, 202, 214, 216, 220, 226, 228, 230, 234, 236, 240, 242, 244, 260, 262, 264, 272, 274, 278, 282, 286

Offset: 1

Author

N. J. A. Sloane, following a suggestion from Paul D. Hanna, Jun 30 2005

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1356

Crossrefs

Cf. A083952, A108337, A108338. See A111363 for another version.

Programs

Mathematica

a[n_] := a[n] = Block[{s = Sum[a[i]*x^i, {i, 0, n - 1}]}, If[ IntegerQ@ Last@ CoefficientList[ Series[ Sqrt[s + x^n], {x, 0, n}], x], 1, 2]]; Union@ Table[ If[ a[n] == 1, n, 0], {n, 0, 300}] (* Robert G. Wilson v, Nov 25 2006 *)

PARI

A108783_upto(N=200)=[k-1 | k<-select(t->t==1, A083952_upto(N),1)] \\ M. F. Hasler, Jan 27 2025