1,1

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".

Since the tribonacci sequence is periodic mod p for any prime p, the sequence is well-defined. - T. D. Noe, Dec 01, 2005

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).

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

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

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

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

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

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

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

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 *)

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

Sequence in context: A101835 A133641 A164094 this_sequence A091574 A063731 A129316

Adjacent sequences: A112266 A112267 A112268 this_sequence A112270 A112271 A112272

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 29 2005

Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Nov 30 2005)