A120818 - OEIS

%I #20 Apr 30 2023 02:11:53

%S 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,

%T 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,

%U 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

%N 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.

%H Seiichi Manyama, <a href="/A120818/b120818.txt">Table of n, a(n) for n = 0..9999</a> (terms 0..999 from Paul D. Hanna)

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

%e x equals the limit of the (n+1) trailing digits of 8^(5^n):

%e 8^(5^0)=(8), 8^(5^1)=327(68), 8^(5^2)=37778931862957161709(568), ...

%e x=...06160350476776695446967548558775834469592160195896736500120813568.

%e x^2=...0557423423230896109004106619977392256259918212890624 (A091664).

%e x^3=...3304553032451441224165530407839804103263499879186432 (A120817).

%e x^4=...9442576576769103890995893380022607743740081787109376 (A018248).

%e x^5=...6695446967548558775834469592160195896736500120813568 = x.

%o (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]}

%Y Cf. A120817, A091664, A018248.

%K base,nonn

%O 0,1

%A _Paul D. Hanna_, Jul 06 2006