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A380818 Numbers k such that the Diophantine equation d_r*x^r + ... + d_0*x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.

%I A380818 #11 Feb 05 2025 22:09:03
%S A380818 0,10,11,12,13,14,15,16,17,18,19,20,22,24,26,28,30,33,36,39,40,44,48,
%T A380818 50,55,60,66,70,77,80,88,90,99,100,110,120,121,130,132,140,143,144,
%U A380818 150,154,156,160,165,168,169,170,176,180,187,190,198,200,210,220,230,231,240,242,250
%N A380818 Numbers k such that the Diophantine equation d_r*x^r + ... + d_0*x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.
%C A380818 For r >= 1, d_r >= 1, numbers k = d_r*10^r are terms. It looks like the solution x (if it exists) is from [-9, 0].
%e A380818 k = 68: the Diophantine equation 6*x + 8 = 0 has no integer solution, thus k = 68 is not a term.
%e A380818 k = 132: the Diophantine equation 1*x^2 + 3*x + 2 = 0 has integer solutions x = -1, x = -2, thus k = 132 is a term.
%Y A380818 Cf. A037124 (for k >= 10).
%K A380818 nonn,base
%O A380818 1,2
%A A380818 _Ctibor O. Zizka_, Feb 04 2025