The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A287513 Numbers whose cyclic permutations are pairwise coprime. 1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 16, 17, 19, 23, 25, 29, 31, 32, 34, 35, 37, 38, 41, 43, 47, 49, 52, 53, 56, 58, 59, 61, 65, 67, 71, 73, 74, 76, 79, 83, 85, 89, 91, 92, 94, 95, 97, 98, 112, 113, 115, 116, 118, 119, 121, 125, 127, 131, 133, 134, 136, 137 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
No term, except 10, contains a '0' digit.
No term contains two even digits.
No term > 9 is a multiple of 3.
No term contains two '5' digits.
This sequence contains A287198.
This sequence does not contain any term > 9 of A084433.
In the scatterplot of the first 10000 terms:
- the jump from a(7128) = 99998 to a(7129) = 111112 is due to the fact that there is no term > 10 starting with "10",
- the dotted lines, for example between a(2545) = 21131 and a(2772) = 29999, are due to the fact that there is no term starting with two even digits,
- these features can be seen at different scales (see scatterplots in Links section).
LINKS
EXAMPLE
The cyclic permutations of 5992 are:
- 5992 = 2^3 * 7 * 107
- 9925 = 5^2 * 397
- 9259 = 47 * 197
- 2599 = 23 * 113.
These values are pairwise coprime, hence 5992 appear in the sequence.
The cyclic permutations of 5776 are:
- 5776 = 2^4 * 19^2,
- 7765 = 5 * 1553,
- 7657 = 13 * 19 * 31,
- 6577 = 6577.
gcd(5776, 7657) = 19, hence 5776 does not appear in the sequence.
PROG
(PARI) is(n) = my (p=n, l=#digits(n)); for (k=1, l-1, n = (n\10) + (n%10)*(10^(l-1)); if (gcd(n, p)>1, return (0)); p = lcm(n, p); ); return (1)
CROSSREFS
Sequence in context: A050724 A336813 A209860 * A194403 A305707 A161979
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 26 2017
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 May 21 17:21 EDT 2024. Contains 372738 sequences. (Running on oeis4.)