login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 the backward value is 0.521, 5^10 = 9765625, so the 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-François Alcover, Dec 21 2012, translated from Robert Israel's Maple program *)

PROG

(Magma) D:=87; e:=6; for d in [2..D-1] do t:=Modexp(5, e, 10^(d+1)); if t div 10^d lt 5 then e+:=2^(d-2); end if; end for; t:=Modexp(5, e, 10^D); IntegerToSequence(t, 10); // Jon E. Schoenfield, Feb 07 2018

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)