

A071988


Triple Peano sequence: a list of triples (x,y,z) starting at (1,1,1); then x'=x+1, y'=y+x, z'=z+y, for x only ranging over the primes


2



2, 2, 2, 3, 4, 4, 5, 11, 15, 7, 22, 42, 11, 56, 176, 13, 79, 299, 17, 137, 697, 19, 172, 988, 23, 254, 1794, 29, 407, 3683, 31, 466, 4526, 37, 667, 7807, 41, 821, 10701, 43, 904, 12384, 47, 1082, 16262, 53, 1379, 23479, 59, 1712, 32568, 61, 1831, 36051, 67, 2212
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OFFSET

1,1


COMMENTS

a(3k+1) are the primes (A000040), by definition.
a(3k+2) are A072205. Second terms are (n^2+n+2)/2 by induction (for n prime).
a(3k) are A072206. Third terms are (n^3+5*n+6)/6 by induction (for n prime).


LINKS

Table of n, a(n) for n=1..56.


EXAMPLE

x'=x+1=1+1=2, y'=y+x=1+1=2, z'=z+y=1+1=2.


MATHEMATICA

seq[n_Integer?Positive] := Module[{fn01 = 1, fn10 = 1, fnout = 1}, Do[{fn10, fn01, fnout} = {fn10 + 1, fn01 + fn10, fn01 + fnout}, {n  1}]; {fn10, fn01, fnout}]; Flatten[ Table[ seq[ Prime[n]], {n, 1, 100}]]


PROG

(PARI) a(n)=subst([x, x*(x1)/2+1, (x^33*x^2+8*x)/6], x, prime(1+(n1)\3))[1+(n1)%3]


CROSSREFS

Cf. A072205 & A072206.
Sequence in context: A079398 A225499 A215473 * A301337 A302404 A029050
Adjacent sequences: A071985 A071986 A071987 * A071989 A071990 A071991


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Jun 17 2002


EXTENSIONS

Edited by Robert G. Wilson v, Jul 03 2002


STATUS

approved



