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A376360
Positions of numbers in A007961 that end in 3.
3
3, 7, 12, 19, 23, 28, 32, 39, 43, 48, 52, 56, 61, 67, 71, 76, 84, 88, 93, 103, 107, 112, 119, 124, 128, 133, 140, 147, 151, 156, 163, 167, 172, 176, 181, 188, 192, 199, 203, 208, 215, 219, 224, 228, 232, 237, 244, 248, 253, 259, 263, 268, 275, 279, 284, 288
OFFSET
1,1
COMMENTS
Every positive integer is in exactly one of these sequences: A376357, A376358, A376359, or this sequence.
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.)
MATHEMATICA
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]]]
t4 = Map[a[#, 4] &, Range[200]]; (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]] (* A376357 *)
p1 = Flatten[Position[m, 1]] (* A376358 *)
p2 = Flatten[Position[m, 2]] (* A376359 *)
p3 = Flatten[Position[m, 3]] (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Sep 25 2024
STATUS
approved