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%I #11 Sep 29 2024 02:38:35
%S 2,5,8,12,17,20,23,26,30,33,38,41,44,47,50,53,57,60,63,68,71,74,80,83,
%T 86,90,93,96,99,103,107,110,113,117,122,125,128,132,138,141,144,148,
%U 155,158,161,165,170,173,176,179,183,188,192,195,198
%N Positions of numbers in A000462 that end in 2.
%C Every positive integer is in exactly one of the following sequences: A376354, A376355, or this sequence.
%C Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9}. (See related conjectures at A376354 and A376355.)
%t a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2) # (# - 1)/2 + # &, Range[Floor[Sqrt[2 n]]]]]][[All, 2]]]
%t t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
%t m = Mod[t3, 10]
%t Table[Flatten[Position[m, r]], {r, 0, 2}]
%t p0 = Flatten[Position[m, 0]] (* A376354 *)
%t p1 = Flatten[Position[m, 1]] (* A376355 *)
%t p2 = Flatten[Position[m, 2]] (* this sequence *)
%t (* _Peter J. C. Moses_, Sep 20 2024 *)
%Y Cf. A000462, A376354, A376355, A376357.
%K nonn,base
%O 1,1
%A _Clark Kimberling_, Sep 25 2024