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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. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

x = 10-adic limit_{n->infty} 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: A036413 A069912 A152306 * A166310 A293030 A109852

Adjacent sequences:  A120814 A120815 A120816 * A120818 A120819 A120820

KEYWORD

base,nonn

AUTHOR

Paul D. Hanna, Jul 06 2006

STATUS

approved

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Last modified February 22 19:54 EST 2019. Contains 320403 sequences. (Running on oeis4.)