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A112618
Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that prime(n) divides T(k).
2
3, 7, 14, 5, 8, 6, 28, 18, 29, 77, 14, 19, 35, 82, 29, 33, 64, 68, 100, 132, 31, 18, 270, 109, 19, 186, 13, 184, 105, 172, 586, 79, 11, 34, 10, 223, 71, 37, 41, 314, 100, 25, 72, 171, 382, 26, 83, 361, 34, 249, 36, 28, 506, 304, 54, 37, 177, 331, 61, 536, 777, 458, 30, 123
OFFSET
1,1
COMMENTS
Brenner proves that every prime divides some tribonacci number T(n). For the similar 3-step Lucas sequence A001644, there are primes (A106299) that do not divide any term.
LINKS
J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
Eric Weisstein's World of Mathematics, Tribonacci Number
FORMULA
a(n) = A112305(prime(n)).
EXAMPLE
Sequence T(n) starts 1,1,2,4,7,13,24,44. For the primes 2,3,7,11,13, it is easy to see that a(1)=3, a(2)=7, a(4)=5, a(5)=8, a(6)=6.
MATHEMATICA
a[0]=0; a[1]=a[2]=1; a[n_]:=a[n]=a[n-1]+a[n-2]+a[n-3]; f[n_]:= Module[{k=2, p=Prime[n]}, While[Mod[a[k], p] != 0, k++ ]; k]; Array[f, 64] (* Robert G. Wilson v *)
CROSSREFS
Equals A112312(n)-1.
Sequence in context: A172291 A343589 A089305 * A058027 A128661 A175339
KEYWORD
nonn
AUTHOR
T. D. Noe, Dec 05 2005
STATUS
approved