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A112312 Least index k such that the n-th prime divides the k-th tribonacci number. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..64.

J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.

Eric Weisstein's World of Mathematics, MathWorld: Tribonacci Number

FORMULA

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).

EXAMPLE

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).

MATHEMATICA

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 *)

CROSSREFS

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

Cf. also A112618 = this sequence minus 1.

Sequence in context: A242519 A174554 A272048 * A076343 A272346 A214440

Adjacent sequences:  A112309 A112310 A112311 * A112313 A112314 A112315

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 29 2005

EXTENSIONS

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

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)