A321289 Digits of the unique 10-adic odd integer x with alternating even and odd digits whose 5-adic valuation is +oo.

5, 2, 1, 8, 7, 0, 5, 0, 7, 2, 7, 2, 3, 2, 3, 4, 7, 4, 1, 6, 5, 4, 1, 0, 9, 8, 1, 0, 9, 0, 7, 6, 3, 6, 3, 8, 3, 2, 9, 2, 7, 6, 3, 6, 7, 0, 5, 8, 1, 6, 1, 0, 9, 6, 7, 0, 7, 8, 3, 4, 9, 2, 9, 2, 9, 2, 7, 4, 5, 8, 9, 8, 5, 0, 3, 4, 7, 6, 7, 4, 5, 6, 5, 8, 9, 8, 7

Offset

0,1

Comments

For n > 0, if n is odd, then a(n) is the unique number in {0, 2, 4, 6, 8} such that A321288(n) + a(n)*5^n divides 5^(n+1); if n is even, then a(n) is the unique number in {1, 3, 5, 7, 9} such that A321288(n) + a(n)*5^n divides 5^(n+1).

The unique 10-adic even integer with alternating even and odd digits whose 5-adic valuation is +oo is given by 10*x. - Jianing Song, Feb 24 2021

Links

Table of n, a(n) for n=0..86.

Formula

For n > 0, a(n) = (A321288(n) - A321288(n-1))/10^n.

a(n) == 1 - n (mod 2).

Example

x = ...72923836367090189014561474323272705078125.

Mathematica

nmax = 87; v[1] = 5; For[i = 2, i <= nmax, i++, For[j = 0, j <= 4, j++, t = v[i-1] + (2j + Mod[i, 2]) 10^(i-1); If[Mod[t, 5^i] == 0, v[i] = t; Break[]]]];
a[0] = 5; a[n_] := (v[n+1] - v[n])/10^n;
Table[a[n], {n, 0, nmax-1}] (* Jean-François Alcover, Nov 23 2018, from PARI *)

Prog

(PARI) seq(n)={my(v=vector(n)); v[1]=5; for(i=2, n, for(j=0, 4, my(t=v[i-1] + (2*j + i%2)*10^(i-1)); if(t%(5^i)==0, v[i]=t; break))); v}
a(n) = if(n, my(j=seq(n+1)); (j[n+1] - j[n])/10^n, 5)

Crossrefs

Cf. A321288.

Sequence in context: A156730 A159549 A011394 * A318380 A318328 A371848

Adjacent sequences: A321286 A321287 A321288 * A321290 A321291 A321292

Keyword

nonn

Author

Jianing Song, Nov 02 2018

Status

approved