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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.

%I A108783 #19 Jan 28 2025 00:57:39
%S A108783 0,2,6,10,12,26,30,32,36,50,52,56,60,62,126,130,132,136,150,152,160,
%T A108783 164,166,170,172,174,176,180,184,192,194,198,200,202,214,216,220,226,
%U A108783 228,230,234,236,240,242,244,260,262,264,272,274,278,282,286
%N 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.
%H A108783 Robert G. Wilson v, <a href="/A108783/b108783.txt">Table of n, a(n) for n = 1..1356</a>
%t A108783 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 *)
%o A108783 (PARI) A108783_upto(N=200)=[k-1 | k<-select(t->t==1, A083952_upto(N),1)] \\ _M. F. Hasler_, Jan 27 2025
%Y A108783 Cf. A083952, A108337, A108338. See A111363 for another version.
%K A108783 nonn
%O A108783 1,2
%A A108783 _N. J. A. Sloane_, following a suggestion from _Paul D. Hanna_, Jun 30 2005