A120818 10-adic integer x=...92160195896736500120813568 satisfying x^5 = x; also x^3 = -x = A120817; (x^2)^3 = x^2 = A091664; (x^4)^2 = x^4 = A018248.

8, 6, 5, 3, 1, 8, 0, 2, 1, 0, 0, 5, 6, 3, 7, 6, 9, 8, 5, 9, 1, 0, 6, 1, 2, 9, 5, 9, 6, 4, 4, 3, 8, 5, 7, 7, 8, 5, 5, 8, 4, 5, 7, 6, 9, 6, 4, 4, 5, 9, 6, 6, 7, 7, 6, 7, 4, 0, 5, 3, 0, 6, 1, 6, 0, 4, 7, 3, 1, 3, 9, 0, 4, 2, 7, 9, 0, 8, 5, 3, 5, 6, 3, 5, 0, 3, 6, 6, 6, 9, 1, 7, 9, 6, 6, 4, 1, 1, 6, 5, 9, 5, 6, 4, 4

Offset: 0

Author

Paul D. Hanna, Jul 06 2006

Keywords

• base
• nonn

Examples

			x equals the limit of the (n+1) trailing digits of 8^(5^n):
8^(5^0)=(8), 8^(5^1)=327(68), 8^(5^2)=37778931862957161709(568), ...
x=...06160350476776695446967548558775834469592160195896736500120813568.
x^2=...0557423423230896109004106619977392256259918212890624 (A091664).
x^3=...3304553032451441224165530407839804103263499879186432 (A120817).
x^4=...9442576576769103890995893380022607743740081787109376 (A018248).
x^5=...6695446967548558775834469592160195896736500120813568 = x.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..9999 (terms 0..999 from Paul D. Hanna)

Crossrefs

Cf. A120817, A091664, A018248.

Programs

PARI

{a(n)=local(b=8,v=[]);for(k=1,n+1,b=b^5%10^k;v=concat(v,(10*b\10^k)));v[n+1]}

Formula

x = 10-adic lim_{n->oo} 8^(5^n).