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Difference between 10-adic numbers defined in A018248 & A018247.
4

%I #17 Jul 27 2017 04:18:06

%S 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,

%T -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,

%U 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

%N Difference between 10-adic numbers defined in A018248 & A018247.

%C 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).

%C Read backwards so as to match their counterparts (A007185 & A016090), A018247(0)+A018248(0) = 11 & A018247(n)+A018248(n) = 9 for all n's > 0 and their product is A076308.

%C All entries must be odd.

%C Is the accumulative sum equally positive and negative, i.e. does the sum equal 0 infinitely often?

%H Seiichi Manyama, <a href="/A075693/b075693.txt">Table of n, a(n) for n = 0..9999</a>

%F a(n) = A018248(n) - A018247(n). - _Seiichi Manyama_, Jul 26 2017

%t (* execute the programming in both A018247 & A018248 *) Reverse[b - a]

%t 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_ *)

%Y Cf. A018248 & A018247.

%K easy,sign,base

%O 0,2

%A _Robert G. Wilson v_, Sep 26 2002