OFFSET
0,1
COMMENTS
The 10-adic numbers a and b defined in this sequence and A018248 satisfy a^2=a, b^2=b, a+b=1, ab=0. - Michael Somos
REFERENCES
W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 1947.
V. deGuerre and R. A. Fairbairn, Jnl. Rec. Math., No. 3, (1968), 173-179.
M. Kraitchik, Sphinx, 1935, p. 1.
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 0..9999
Anthony Edey, Automorphic numbers, taken from Madachy's Mathematical Recreations, Dover 1979.
V. deGuerre and R. A. Fairbairn, Automorphic numbers, Jnl. Rec. Math., 1 (No. 3, 1968), 173-179.
MathOverflow, Distribution of digits of pq-adic idempotents (aka “automorphic numbers”), 2014.
Eric Weisstein's World of Mathematics, Automorphic numbers.
FORMULA
x = 10-adic lim_{n->oo} 5^(2^n) mod 10^(n+1). - Paul D. Hanna, Jul 08 2006
EXAMPLE
x = ...0863811000557423423230896109004106619977392256259918212890625.
MATHEMATICA
a = {5}; f[n_] := Block[{k = 0, c}, While[c = FromDigits[Prepend[a, k]]; Mod[c^2, 10^n] != c, k++ ]; a = Prepend[a, k]]; Do[ f[n], {n, 2, 105}]; Reverse[a]
With[{n = 150}, Reverse[IntegerDigits[PowerMod[5, 2^n, 10^n]]]] (* IWABUCHI Yu(u)ki, Feb 16 2024 *)
PROG
(PARI) a(n)=local(t=5); for(k=1, n+1, t=t^2%10^k); t\10^n \\ Paul D. Hanna, Jul 08 2006
(PARI) Vecrev(digits(lift(chinese(Mod(1, 2^100), Mod(0, 5^100))))) \\ Seiichi Manyama, Aug 07 2019
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Yoshihide Tamori (yo(AT)salk.edu)
EXTENSIONS
More terms from David W. Wilson
Edited by David W. Wilson, Sep 26 2002
STATUS
approved