A112618 -id:A112618 - cp's OEIS frontend

A112312 Least index k such that the n-th prime divides the k-th tribonacci number.

4, 8, 15, 6, 9, 7, 29, 19, 30, 78, 15, 20, 36, 83, 30, 34, 65, 69, 101, 133, 32, 19, 271, 110, 20, 187, 14, 185, 106, 173, 587, 80, 12, 35, 11, 224, 72, 38, 42, 315, 101, 26, 73, 172, 383, 27, 84, 362, 35, 250, 37, 29, 507, 305, 55, 38, 178, 332, 62, 537, 778, 459, 31, 124

Offset: 1

Jonathan Vos Post, Nov 29 2005

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). See A112618 for another version.

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.

			a(1) = 4 because prime(1) = 2 and tribonacci( 4) = 2.
a(2) = 8 because prime(2) = 3 and tribonacci( 8) = 24 = 3 * 2^3.
a(3) = 15 because prime(3) = 5 and tribonacci(15) = 1705 = 5 *(11 * 31).
a(4) = 6 because prime(4) = 7 and tribonacci( 6) = 7.
a(5) = 9 because prime(5) = 11 and tribonacci( 9) = 44 = 11 * 4.
a(6) = 7 because prime(6) = 13 and tribonacci( 7) = 13.
a(7) = 29 because prime(7) = 17 and tribonacci(29) = 8646064 = 17 *(2^4 * 7 * 19 * 239).

J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
Eric Weisstein's World of Mathematics, MathWorld: Tribonacci Number

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

Cf. also A112618 = this sequence minus 1.

a[0] = a[1] = 0; 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 *)

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).

Corrected and extended by Robert G. Wilson v, Dec 01 2005

cp's OEIS Frontend

A112312 Least index k such that the n-th prime divides the k-th tribonacci number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions