A112269 - OEIS

%I #12 Mar 17 2015 23:02:21

%S 5,8,15,13,9,19,29,19,30,78,15,20,36,83,30,34,65,69,101,133,32,19,271,

%T 110,20,187,14,185,106,173,587,80,12,35,46,224,72,38,42,315,101,26,73,

%U 172,383,27,84,362,35,250,37,29,507,305,55,38,178,332,62,537,778,459,31

%N Least index k such that the n-th prime properly divides the k-th tribonacci number.

%C The tribonacci numbers are indexed so that trib(0) = trib(1) = 0, trib(2) = 1, for n>2: trib(n) = trib(n-1) + trib(n-2) + trib(n-3). "Properly divides" means that this sequence is "Least index k such that the n-th prime divides the k-th tribonacci number not itself the n-th prime".

%C Since the tribonacci sequence is periodic mod p for any prime p, the sequence is well-defined. - _T. D. Noe_, Dec 01 2005

%F a(n) = minimum k such that prime(n) | A000073(k) and A000073(k) > prime(n). a(n) = minimum k such that A000040(n) | A000073(k) and A000073(k) > A000040(n).

%e a(1) = 5 because prime(1) = 2 and, although tribonacci(4) = 2, the first tribonacci number properly divided by 2 is tribonacci(5) = 4.

%e a(2) = 8 because prime(2) = 3 and tribonacci(8) = 24 = 2^3 * 3.

%e a(3) = 15 because prime(3) = 5 and tribonacci(15) = 1705 = 5 * 11 * 31.

%e a(4) = 13 because prime(4) = 7 and tribonacci(13) = 504 = 2^3 * 3^2 * 7.

%e a(5) = 9 because prime(5) = 11 and tribonacci(9) = 44 = 2^2 * 11.

%e a(6) = 19 because prime(6) = 13 and tribonacci(19) = 19513 = 13 * 19 * 79.

%e a(7) = 29 because prime(7) = 17 and tribonacci(29) = 646064 = 2^4 * 7 * 17 * 19 * 239.

%t a[0] = a[1] = 0; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; f[n_] := Block[{k = 1, p = Prime[n]}, While[ Mod[a[k], p] != 0 || p >= a[k], k++ ]; k]; Array[f, 63] (* _Robert G. Wilson v_ *)

%Y Cf. A000040, A000045, A000073, A000204, A001644, A053028, A106299, A112312.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 29 2005

%E Corrected and extended by _Robert G. Wilson v_, Nov 30 2005