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A376360 Positions of numbers in A007961 that end in 3.

%I A376360 #7 Sep 28 2024 12:58:50
%S A376360 3,7,12,19,23,28,32,39,43,48,52,56,61,67,71,76,84,88,93,103,107,112,
%T A376360 119,124,128,133,140,147,151,156,163,167,172,176,181,188,192,199,203,
%U A376360 208,215,219,224,228,232,237,244,248,253,259,263,268,275,279,284,288
%N A376360 Positions of numbers in A007961 that end in 3.
%C A376360 Every positive integer is in exactly one of these sequences: A376357, A376358, A376359, or this sequence.
%C A376360 Conjecture: {a(n+1) - a(n) : n >= 1} = {4,5,6,7,8,9,10,11,13}. It has been checked that a(n+1) - a(n) is not 12 for 1<=n<=300000.  (See related conjectures at A376357, A376358, and A376359.)
%t A376360 a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
%t A376360 Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
%t A376360 t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
%t A376360 m = Mod[t4, 10];
%t A376360 Table[Flatten[Position[m, r]], {r, 0, 2}]
%t A376360 p0 = Flatten[Position[m, 0]]  (* A376357 *)
%t A376360 p1 = Flatten[Position[m, 1]]  (* A376358 *)
%t A376360 p2 = Flatten[Position[m, 2]]  (* A376359 *)
%t A376360 p3 = Flatten[Position[m, 3]]  (* this sequence *)
%t A376360 (* _Peter J. C. Moses_, Sep 20 2024 *)
%Y A376360 Cf. A007961, A376354, A376357, A376358, A376359.
%K A376360 nonn,base
%O A376360 1,1
%A A376360 _Clark Kimberling_, Sep 25 2024