

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
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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 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, l1, n = (n\10) + (n%10)*(10^(l1)); if (gcd(n, p)>1, return (0)); p = lcm(n, p); ); return (1)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



