A388148 - OEIS

A388148

Decimal expansion of the tetrahedral root of 2.

1, 4, 3, 4, 8, 4, 1, 3, 6, 8, 2, 1, 6, 9, 0, 0, 8, 2, 4, 9, 5, 4, 6, 0, 6, 7, 5, 3, 4, 8, 8, 4, 4, 3, 5, 0, 1, 2, 8, 9, 5, 4, 2, 9, 6, 6, 2, 3, 5, 2, 0, 2, 2, 8, 8, 1, 0, 8, 4, 7, 3, 2, 5, 4, 8, 1, 4, 0, 6, 0, 3, 9, 9, 5, 5, 3, 4, 8, 4, 4, 5, 8, 7, 8, 5, 5, 7, 4, 2, 6, 9, 7, 8, 9, 2, 6, 9, 8, 0, 5, 4, 9, 7, 0, 3

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OFFSET

1,2

COMMENTS

The real solution to x*(x+1)*(x+2)/6 = 2.

LINKS

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Wikipedia, Tetrahedral roots and tests for tetrahedral numbers

Index entries for algebraic numbers, degree 3.

FORMULA

Equals ((sqrt(2913) + 54) / 9)^(1/3) + ((162 - 3*sqrt(2913)) / 27)^(1/3) - 1.

EXAMPLE

1.4348413682169008249546067534884435...

MATHEMATICA

N[-1 + (1/3) (162 - 3 Sqrt[2913])^(1/3) + (54 + Sqrt[2913])^(1/3)/3^(2/3), 79]

PROG

(PARI) (sqrt(2913)+54)^(1/3)/3^(2/3)+(162-3*sqrt(2913))^(1/3)/3-1

CROSSREFS

Cf. A000292, A002193 (square root of 2), A222133 (triangular root of 2), A188934 (hexagonal root of 2).

Platonic figurate roots of 2: A002580 (cube root), this sequence (tetrahedral root), A389133 (octahedral root), A389134 (icosahedral root), A389135 (dodecahedral root).

Sequence in context: A339409 A075246 A257840 * A132984 A277528 A358736

Adjacent sequences: A388145 A388146 A388147 * A388149 A388150 A388151

KEYWORD

nonn,cons

AUTHOR

Kelvin Voskuijl, Sep 15 2025

STATUS

approved