A258258 - OEIS

A258258

Least number k having exactly n representations as a sum of the minimal number of triangular numbers, A000217.

1, 16, 40, 75, 52, 82, 166, 178, 147, 217, 334, 247, 481, 634, 457, 516, 921, 646, 1047, 1132, 822, 787, 2110, 1351, 1537, 1542, 1402, 1192, 1666, 1696, 2137, 1759, 1876, 2271, 1792, 2712, 2587, 3216, 3909, 2782, 3007, 2956, 4242, 3397, 3682, 4039, 3607, 3601

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OFFSET

1,2

COMMENTS

Fermat's polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. The triangular case was proved in 1796 by Gauss (Eureka theorem), stating that every positive integer is the sum of at most three triangular numbers. This sequence is based on this representation as a sum of the minimal number of triangular numbers.

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

a(2) = 16 = 1 + 15 = 6 + 10 is the smallest number with two representations.

a(3) = 40 = 1 + 3 + 36 = 6 + 6 + 28 = 10 + 15 + 15 is the smallest number with three representations.

a(4) = 75 = 3 + 6 + 66 = 3 + 36 + 36 = 10 + 10 + 55 = 15 + 15 + 45 is the smallest number with four representations.

CROSSREFS

Cf. A141490, A258257.

Sequence in context: A332519 A177723 A174321 * A086046 A184030 A350284

Adjacent sequences: A258255 A258256 A258257 * A258259 A258260 A258261

KEYWORD

nonn

AUTHOR

Martin Renner, May 24 2015

STATUS

approved