This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112618 #15 Feb 16 2025 08:32:59
%S A112618 3,7,14,5,8,6,28,18,29,77,14,19,35,82,29,33,64,68,100,132,31,18,270,
%T A112618 109,19,186,13,184,105,172,586,79,11,34,10,223,71,37,41,314,100,25,72,
%U A112618 171,382,26,83,361,34,249,36,28,506,304,54,37,177,331,61,536,777,458,30,123
%N A112618 Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that prime(n) divides T(k).
%C A112618 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.
%H A112618 T. D. Noe, <a href="/A112618/b112618.txt">Table of n, a(n) for n=1..1000</a>
%H A112618 J. L. Brenner, <a href="http://www.jstor.org/stable/2307216">Linear Recurrence Relations</a>, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
%H A112618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TribonacciNumber.html">Tribonacci Number</a>
%F A112618 a(n) = A112305(prime(n)).
%e A112618 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.
%t A112618 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_ *)
%Y A112618 Equals A112312(n)-1.
%K A112618 nonn
%O A112618 1,1
%A A112618 _T. D. Noe_, Dec 05 2005