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A302253 Positions of 3 in A190436.

%I A302253 #14 Apr 13 2018 06:01:35
%S A302253 8,21,29,42,55,63,76,97,110,118,131,144,152,165,186,199,207,220,241,
%T A302253 254,262,275,288,296,309,330,343,351,364,377,385,398,406,419,432,440,
%U A302253 453,474,487,495,508,521,529,542,563,576,584,597,618,631,639,652,665,673,686,707,720,728
%N A302253 Positions of 3 in A190436.
%C A302253 Write a(n) = [(bn+c)r] - b[nr] - [cr]. If r>0 and b and c are integers satisfying b >= 2 and 0 <= c <= b-1, then 0 <= a(n) <= b.  The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b.  These b+1 position sequences comprise a partition of the positive integers.
%C A302253 Examples:
%C A302253 (golden ratio,2,0):  A078588, A005653, A005652
%C A302253 (golden ratio,2,1):  A190427-A190430
%C A302253 (golden ratio,3,0):  A140397-A190400
%C A302253 (golden ratio,3,1):  A140431-A190435
%C A302253 (golden ratio,3,2):  A140436-A190439
%C A302253 (golden ratio,4,c):  A140440-A190461
%H A302253 G. C. Greubel, <a href="/A302253/b302253.txt">Table of n, a(n) for n = 1..20000</a>
%t A302253 r = GoldenRatio; b = 3; c = 2;
%t A302253 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A302253 t = Table[f[n], {n, 1, 500}] (* A190436 *)
%t A302253 Flatten[Position[t, 0]] (* A190437 *)
%t A302253 Flatten[Position[t, 1]] (* A190438 *)
%t A302253 Flatten[Position[t, 2]] (* A190439 *)
%t A302253 Flatten[Position[t, 3]] (* A302253 *)
%Y A302253 Cf. A190436, A190437, A190438, A190439.
%K A302253 nonn
%O A302253 1,1
%A A302253 _G. C. Greubel_, Apr 04 2018