|
| |
|
|
A075693
|
|
Difference between 10-adic numbers defined in A018248 & A018247.
|
|
2
|
|
|
|
1, 5, -3, 9, -9, -7, 5, 7, 5, -7, 7, -9, -9, -1, 5, -3, -1, 5, 5, -9, 3, -5, -5, -9, -9, 7, -3, -3, 9, 7, 1, 9, 9, -9, 9, 7, -3, -9, -7, 9, 3, 5, 3, 5, 1, 3, 5, 1, -5, -1, -1, 9, 9, 9, 7, 7, -7, 3, -3, -7, 9, -7, -1, -9, 9, -1, -3, -3, 7, 5, -3, 9, 9, -9, -7, -9, 9, -1, -7, 3, -9, 5, 9, -7
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Numbers in A018247 and A018248 are known as automorphic numbers in base 10, meaning that the infinite integers a=(...256259918212890625) or b=(...743740081787109376) provides a nontrivial solution to x*x == x (mod any power of 10).
Read backwards so as to match their counterparts (A007185 & A016090), A018247(1)+A018248(1) = 11 & A018247(n)+A018248(n) = 9 for all n's > 1 and their product is A076308.
All entries must be odd.
Is the accumulative sum equally positive and negative, i.e. does the sum equal 0 infinitely often?
|
|
|
LINKS
|
Table of n, a(n) for n=1..84.
|
|
|
MATHEMATICA
|
(* execute the programming in both A018247 & A018248 *) Reverse[b - a]
aa[n_] := For[t = 5; k = 1, True, k++, t = Mod[t^2, 10^k]; If[k == n, Return[ Quotient[t, 10^(n-1)]]]]; bb[n_] := Reap[ For[t = 6; k = 1, k <= n , k++, t = Mod[t^5, 10^k]; Sow[ Quotient[10*t, 10^k]]]][[2, 1, n]]; a[n_] := bb[n] - aa[n]; Table[a[n], {n, 1, 84}](* Jean-François Alcover, May 25 2012, after Paul D. Hanna *)
|
|
|
CROSSREFS
|
Cf. A018248 & A018247.
Sequence in context: A201938 A201410 A019955 * A198134 A082454 A108245
Adjacent sequences: A075690 A075691 A075692 * A075694 A075695 A075696
|
|
|
KEYWORD
|
easy,sign,base
|
|
|
AUTHOR
|
Robert G. Wilson v, Sep 26 2002
|
|
|
STATUS
|
approved
|
| |
|
|
