A120818 - OEIS

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

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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 lim_{n->oo} 8^(5^n).

EXAMPLE

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.

PROG

(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]}

CROSSREFS

Cf. A120817, A091664, A018248.

Sequence in context: A092033 A061360 A353962 * A125579 A202258 A367409

Adjacent sequences: A120815 A120816 A120817 * A120819 A120820 A120821

KEYWORD

base,nonn

AUTHOR

Paul D. Hanna, Jul 06 2006

STATUS

approved