A256526 Smallest exponent m such that 2^m begins and ends with the same n digits, allowing any other digits in between.

16, 24, 458, 18341, 16641, 1116830, 10971256, 105969200, 193295556, 48221950695, 72585186028

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Example

2^24 = 16777216 starts and ends with the same two digits.
Solution details:
A is the substring of beginning and ending digits
B is the total number of digits in 2^a(n)
n.......a(n)..........A..........B
1.........16..........6..........5
2.........24.........16..........8
3........458........744........138
4......18341.......1552.......5522
5......16641......27552.......5010
6....1116830.....213824.....336200
7...10971256....1399936....3302678
8..105969200...65541376...31899908 - Lars Blomberg, May 07 2015

Prog

(Magma) lst:=[]; c:=Log(10, 2); for n in [1..5] do k:=Ceiling(2*n/c); t:=0; while t eq 0 do m:=2^k mod 10^n; if #Intseq(m) eq n then if Truncate(2^k/10^(Floor(k*c+1)-n)) eq m then Append(~lst, k); t:=1; end if; end if; k+:=1; end while; end for; lst;

Crossrefs

Sequence in context: A120468 A166629 A066261 * A243914 A226296 A070571

Adjacent sequences: A256523 A256524 A256525 * A256527 A256528 A256529

Keyword

nonn,base,more

Author

Arkadiusz Wesolowski, Apr 01 2015

Extensions

a(6)-a(8) from Lars Blomberg, May 07 2015

a(9)-a(11) from Hiroaki Yamanouchi, Jun 03 2015

Status

approved