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A216439 Smallest k such that k*n^3 + 1 is an n-th power. 3
1, 1, 37, 791, 95051, 111748, 2277696793, 484679258335, 229930796172439, 79792266297612, 66954547910007962117, 337165646545, 45082285083777592171142467, 2379140952844779936142872, 60722942736706550906445847537201, 78033832840595333890814363993704319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..216

EXAMPLE

a(3) = 37 because 37*3^3 + 1 = 1000 = 10^3.

MAPLE

f:= proc(n) local S, x;

  S:= subs(1=n^3+1, map(t -> rhs(op(t)), [msolve(x^n-1, n^3)]));

  x:= min(S);

  (x^n-1)/n^3

end proc:

f(1):= 1:

map(f, [$1..20]); # Robert Israel, Aug 26 2020

MATHEMATICA

a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^3], k++ ]; AppendTo[a, (k^n-1)/n^3], {n, 1, 20}]; a

CROSSREFS

Cf. A076943, A193746.

Sequence in context: A258463 A320551 A211834 * A333065 A251105 A144511

Adjacent sequences:  A216436 A216437 A216438 * A216440 A216441 A216442

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 10 2012

STATUS

approved

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Last modified July 23 11:07 EDT 2021. Contains 346259 sequences. (Running on oeis4.)