A086105 Adding, multiplying and exponentiating cycle of the previous two terms similar to A039941.

0, 1, 1, 1, 1, 2, 2, 4, 6, 24, 4738381338321616896, 4738381338321616920, 22452257707354557353808363243511480320

Offset: 1

Author

Anthony Peterson (civ2buf(AT)ricochet.com), Jul 09 2003

Keywords

• easy
• nonn

Examples

			a(11) = a(9)^a(10)=6^24 because 11 mod 3 is 2.
		

Crossrefs

Cf. A039941.

Programs

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,Which[Mod[n+1,3]==0,a+b,Mod[n+1,3]==1,a*b,True,a^b]}; NestList[ nxt,{2,0,1},12][[;;,2]] (* Harvey P. Dale, Oct 04 2023 *)

Formula

a(1)=0, a(2)=1, a(n): if n mod 3 is 0: a(n)=a(n-2) + a(n-1), if n mod 3 is 1: a(n)=a(n-2) * a(n-1), if n mod 3 is 2: a(n)=a(n-2)^a(n-1).

Extensions

The next 2 terms are (6^24)^((6^24)*(6^24+24)) and (6^24)^((6^24) * (6^24 + 24)) + (6^24) * (6^24 + 24).