A376357 - OEIS

%I #7 Sep 28 2024 12:59:35

%S 4,8,9,13,16,20,24,25,29,33,34,36,40,44,45,49,53,57,58,62,64,68,72,73,

%T 77,80,81,85,89,90,94,97,100,104,108,109,113,116,120,121,125,129,130,

%U 134,137,141,144,148,152,153,157,160,164,168,169,173,177,178,182

%N Positions of numbers in A007961 that end in 0.

%C Every positive integer is in exactly one of these sequences: this sequence, A376358, A376359, or A376360.

%C Conjecture: {a(n+1) - a(n) : n >= 1} = {1,2,3,4}. (See related conjectures at A376358-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]]  (* this sequence *)

%t p1 = Flatten[Position[m, 1]]  (* A376358 *)

%t p2 = Flatten[Position[m, 2]]  (* A376359 *)

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

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

%Y Cf. A007961, A376354, A376358, A376359, A376360.

%K nonn,base

%O 1,1

%A _Clark Kimberling_, Sep 25 2024