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

Author

Roger L. Bagula, Jun 17 2002

Keywords

• nonn

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).

Examples

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

Crossrefs

Cf. A072205 & A072206.

Programs

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}]]

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]

Extensions

Edited by Robert G. Wilson v, Jul 03 2002