A338482 Least number of centered triangular numbers that sum to n.

1, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5

Offset

1,2

Comments

It appears that a(n) = 3 for n == 0 (mod 3), 1 <= a(n) <= 4 for n == 1 (mod 3), and 2 <= a(n) <= 5 for n == 2 (mod 3). - Robert Israel, Nov 13 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Centered Triangular Number

Index entries for sequences related to centered polygonal numbers

Maple

f:= proc(n) option remember; local r, i;
    r:= sqrt(24*n-15)/6+1/2;
    if r::integer then return 1 fi;
    1+min(seq(procname(n-(3*i*(i-1)/2+1)), i=1..floor(r)))
end proc:
map(f, [$1..200]); # Robert Israel, Nov 13 2020

Mathematica

f[n_] := f[n] = Module[{r}, r = Sqrt[24n-15]/6+1/2; If[IntegerQ[r], Return[1]]; 1+Min[Table[f[n-(3i*(i-1)/2+1)], {i, 1, Floor[r]}]]];
Map[f, Range[200]] (* Jean-François Alcover, Sep 16 2022, after Robert Israel *)

Crossrefs

Cf. A005448, A061336, A101412, A104246, A234533, A338484.

Sequence in context: A096436 A053610 A264031 * A104246 A281367 A007720

Adjacent sequences: A338479 A338480 A338481 * A338483 A338484 A338485

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 29 2020

Status

approved