A376359 - OEIS

%I #7 Sep 28 2024 12:59:12

%S 2,6,11,15,18,22,27,31,38,42,47,51,55,60,66,70,75,79,83,87,92,96,99,

%T 102,106,111,115,118,123,127,132,136,139,143,146,150,155,159,162,166,

%U 171,175,180,184,187,191,198,202,207,211,214,218,223,227,231,236,240

%N Positions of numbers in A007961 that end in 2.

%C Every positive integer is in exactly one of these sequences: A376357, A376358, this sequence, or A376360.

%C Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9,10}. (See related conjectures at A376357, A376358, and A376360.)

%t a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,

%t Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]

%t t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)

%t m = Mod[t4, 10];

%t Table[Flatten[Position[m, r]], {r, 0, 2}]

%t p0 = Flatten[Position[m, 0]]  (* A376357 *)

%t p1 = Flatten[Position[m, 1]]  (* A376359 *)

%t p2 = Flatten[Position[m, 2]]  (* this sequence *)

%t p3 = Flatten[Position[m, 3]]  (* A376360 *)

%t (* _Peter J. C. Moses_, Sep 20 2024 *)

%Y Cf. A007961, A376354, A376357, A376358, A376360.

%K nonn,base

%O 1,1

%A _Clark Kimberling_, Sep 25 2024