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
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 2000 terms
Rémy Sigrist, Scatterplot of the first 10000 terms
Rémy Sigrist, Scatterplot of the first 150000 terms
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 26 2017
STATUS
approved