cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Seyed Ali Tavakoli-Nabavi

Seyed Ali Tavakoli-Nabavi's wiki page.

Seyed Ali Tavakoli-Nabavi has authored 1 sequences.

A255577 Numbers n not coprime to 10 such that there exists an integer k > 1 where n^k contains n as its last digits in base 10.

Original entry on oeis.org

2, 4, 5, 6, 8, 12, 16, 24, 25, 28, 32, 36, 44, 48, 52, 56, 64, 68, 72, 75, 76, 84, 88, 92, 96, 104, 112, 125, 128, 136, 144, 152, 168, 176, 184, 192, 208, 216, 224, 232, 248, 256, 264, 272, 288, 296, 304, 312, 328
Offset: 1

Views

Author

Seyed Ali Tavakoli-Nabavi, May 05 2015

Keywords

Comments

Intersection of A065502 (numbers not coprime with 10) and A072495 (k-morphic numbers).
Also defined as all n not coprime with 10 where there exists k > 1 such that n^k mod 10^floor(log_10(n)) = n.
For n > 1, a(n) <= a(n-1) + 2^(ceiling(log_10(a(n))) + 1) (conjectured).
For a(n) >= 10^k where k >= 1, there exists a(m) = a(n) mod 10^j where m < n and j < k.
From Robert Israel, May 14 2015: (Start)
n with d digits is in the sequence if and only if n is either divisible by 2^d but not by 5, or divisible by 5^d but not by 2.
For d >= 2 the number of terms with d digits is 4*5^(d-1) + 2^(d-1) - 4*floor(5^d/50) - floor(2^d/20) - x(d) where x(d) = 3 if d == 2 or 3 mod 4, 2 otherwise.
(End)

Examples

			For n = 2, we have n^5 = 2^5 = 32, whose last digit is 2 = n, so 2 is in the sequence.
For n = 3, we have n^5 = 3^5 = 243, so 3 is in the sequence.
For n = 4, we have n^3 = 4^3 = 64, so 4 is in the sequence.
...
As a counterexample, n = 41 is not in the sequence because it is coprime with 10, even though we have 41^6 = 4750104241, whose last 2 digits are 41.

Links

Crossrefs

Cf. A065502, A072495.

Programs

  • Maple
    F:= d -> (seq(seq(2^d*(5*j+i),i=1..4),j=0..5^(d-1)-1), seq(5^d*(2*j+1),j=0..2^(d-1)-1)):
sort(convert({seq(F(d),d=1..4)},list)); # Robert Israel, May 14 2015
  • Tcl
    See a255577.tcl in LINKS.

Formula

For n > 6, a(n) > 2n since no term is divisible by 10 (but all are divisible by either 2 or 5). - Charles R Greathouse IV, May 13 2015

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.