A075693 Difference between 10-adic numbers defined in A018248 & A018247.

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

Offset: 0

Author

Robert G. Wilson v, Sep 26 2002

Keywords

• easy
• sign
• base

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(0)+A018248(0) = 11 & A018247(n)+A018248(n) = 9 for all n's > 0 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

• Seiichi Manyama, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A018248 & A018247.

Programs

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 *)

Formula

a(n) = A018248(n) - A018247(n). - Seiichi Manyama, Jul 26 2017