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A158624 Upper limit of backward value of 5^n. 5
5, 2, 6, 5, 6, 7, 9, 5, 7, 8, 7, 9, 6, 9, 9, 7, 6, 5, 7, 8, 8, 5, 5, 7, 6, 9, 7, 5, 9, 9, 5, 7, 8, 9, 5, 8, 6, 7, 7, 5, 6, 5, 6, 9, 5, 7, 5, 6, 6, 9, 6, 7, 7, 6, 7, 6, 8, 8, 5, 8, 5, 6, 7, 5, 8, 9, 6, 6, 7, 5, 9, 5, 7, 9, 8, 6, 8, 8, 7, 9, 5, 8, 8, 5, 8, 5, 9, 5, 5, 8, 9, 7, 7, 9, 7, 7, 9, 6, 7, 6, 8, 9, 7, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Digits are all in {5,6,7,8,9} after 2nd term.

The other limit, related to odd n, is in A158625.

The first digit of the backward value of 5^n is always a(0)=5. The second digit is a(-1)=2 from n=2 on. The third digit is a(-2)=6 for all even n>=4. The fourth digit is a(-3)=5 for n=6+4k, k>=0. The fifth digit is a(-4)=6 for n=10+8k, k>=0. The 6th digit is a(-5)=7 for n=10+16k, k>=0. The 7th digit is a(-6)=9 for n=10+32k, k>=0.

LINKS

Robert Israel, Table of n, a(n) for n = 0..999

EXAMPLE

5^3 = 125 so backward value is 0.521, 5^10 = 9765625, so backward value is 0.5265679. The upper limit of all values is a constant, which appears to be 0.5265679578796997657885576975995789586775656...

MAPLE

A158624:= proc(N)

local m, n, A;

m[2]:= 3;

for n from 3 to N do

  A:= 5&^m[n-1] mod 10^n;

  if A > 5*10^(n-1) then m[n]:= m[n-1]

  else m[n]:= m[n-1]+2^(n-3)

  end if

end do:

convert(5&^m[N] mod 10^(N), base, 10);

end proc; # Robert Israel, Apr 01 2012

MATHEMATICA

A158624[k_] := Module[{m, n, a}, m[2] = 3; For[n = 3, n <= k, n++, a = PowerMod[5, m[n-1], 10^n]; If[ a > 5*10^(n-1), m[n] = m[n-1], m[n] = m[n-1] + 2^(n-3)]]; IntegerDigits[PowerMod[5, m[k], 10^k]] // Reverse]; A158624[105] (* Jean-Fran├žois Alcover, Dec 21 2012, translated from Robert Israel's Maple program *)

CROSSREFS

Cf. A158625, A071583, A145679.

Sequence in context: A211015 A077141 A276566 * A021659 A011506 A054400

Adjacent sequences:  A158621 A158622 A158623 * A158625 A158626 A158627

KEYWORD

cons,nonn,base,nice

AUTHOR

Simon Plouffe, Mar 23 2009

STATUS

approved

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Last modified June 22 07:47 EDT 2017. Contains 288605 sequences.