A071568 Smallest k>n such that n^3+1 divides k*n^2+1.

1, 3, 11, 31, 69, 131, 223, 351, 521, 739, 1011, 1343, 1741, 2211, 2759, 3391, 4113, 4931, 5851, 6879, 8021, 9283, 10671, 12191, 13849, 15651, 17603, 19711, 21981, 24419, 27031, 29823, 32801, 35971, 39339, 42911, 46693, 50691, 54911, 59359

Offset: 0

Author

Benoit Cloitre, May 31 2002

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A101220.

Programs

Mathematica

sk[n_]:=Module[{k=n+1,n2=n^2,n3=n^3+1},While[!Divisible[k*n2+1,n3], k++]; k]; Array[sk,40] (* Harvey P. Dale, Jun 13 2013 *)

PARI

for(n=1,50,s=n+1; while((s*n^2+1)%(n^3+1)>0,s++); print1(s,","))

Formula

a(n) = n^3+n+1.

a(n+1) = A101220(n, n+1, 4).

G.f.: (1 - x + 5*x^2 + x^3)/(1 - x)^4. - Philippe Deléham, Jun 06 2015

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, May 04 2021

E.g.f.: exp(x)*(1 + 2*x + 3*x^2 + x^3). - Stefano Spezia, Jul 21 2025

Extensions

a(0) from Philippe Deléham, Jun 06 2015