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, 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

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*(x-1)/2+1, (x^3-3*x^2+8*x)/6], x, prime(1+(n-1)\3))[1+(n-1)%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