

A071568


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


8



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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..39.
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1)


FORMULA

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


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 *)


PROG

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


CROSSREFS

a(n+1) = A101220(n, n+1, 4).
Sequence in context: A277167 A277049 A261148 * A097081 A093406 A107587
Adjacent sequences: A071565 A071566 A071567 * A071569 A071570 A071571


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, May 31 2002


EXTENSIONS

a(0) from Philippe Deléham, Jun 06 2015


STATUS

approved



