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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 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe, Table of n, a(n) for n=1..1000 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 Adjacent sequences:  A112615 A112616 A112617 * A112619 A112620 A112621 KEYWORD nonn AUTHOR T. D. Noe, Dec 05 2005 STATUS approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)