A120817 10-adic integer x=...07839804103263499879186432 satisfying x^5 = x; also x^3 = -x = A120818; (x^2)^3 = x^2 = A091664; (x^4)^2 = x^4 = A018248.

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

Offset

0,1

Links

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

Patrick A. Thomas, Solutions to x^5=x up to base 100

Formula

x = 10-adic limit_{n->infinity} 2^(5^n).

Example

x equals the limit of the (n+1) trailing digits of 2^(5^n):
2^(5^0)=(2), 2^(5^1)=(32), 2^(5^2)=33554(432),
2^(5^3)=4253529586511730793292182592897102(6432), ...
x=...93839649523223304553032451441224165530407839804103263499879186432.
x^2=...0557423423230896109004106619977392256259918212890624 (A091664).
x^3=...6695446967548558775834469592160195896736500120813568 (A120818).
x^4=...9442576576769103890995893380022607743740081787109376 (A018248).
x^5=...3304553032451441224165530407839804103263499879186432 = x.

Prog

(PARI) {a(n)=local(b=2, v=[]); for(k=1, n+1, b=b^5%10^k; v=concat(v, (10*b\10^k))); v[n+1]}
(PARI) {a(n)=if(n<0, 0, lift(chinese(Mod(truncate( teichmuller(2+O(5^(n+1)))), 5^(n+1)), Mod(0, 2^(n+1))))\10^n)} /* Michael Somos, Oct 03 2006 */

Crossrefs

x^5 = x: this sequence (...6432), A120818 (...3568), A290372 (...5807), A290373 (...2943), A290374 (...7057), A290375 (...4193).

Cf. A091664, A018248.

Sequence in context: A069912 A351329 A152306 * A327887 A339361 A166310

Adjacent sequences: A120814 A120815 A120816 * A120818 A120819 A120820

Keyword

base,nonn

Author

Paul D. Hanna, Jul 06 2006

Status

approved