

A112269


Least index k such that the nth prime properly divides the kth tribonacci number.


1



5, 8, 15, 13, 9, 19, 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, 46, 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
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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(n1) + trib(n2) + trib(n3). "Properly divides" means that this sequence is "Least index k such that the nth prime divides the kth tribonacci number not itself the nth prime".
Since the tribonacci sequence is periodic mod p for any prime p, the sequence is welldefined.  T. D. Noe, Dec 01 2005


LINKS

Table of n, a(n) for n=1..63.


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) = 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.


MATHEMATICA

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 *)


CROSSREFS

Cf. A000040, A000045, A000073, A000204, A001644, A053028, A106299, A112312.
Sequence in context: A246319 A302649 A286835 * A314527 A314528 A091574
Adjacent sequences: A112266 A112267 A112268 * A112270 A112271 A112272


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 29 2005


EXTENSIONS

Corrected and extended by Robert G. Wilson v, Nov 30 2005


STATUS

approved



