A287513 - OEIS

%I #14 Nov 23 2019 02:39:36

%S 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,

%T 47,49,52,53,56,58,59,61,65,67,71,73,74,76,79,83,85,89,91,92,94,95,97,

%U 98,112,113,115,116,118,119,121,125,127,131,133,134,136,137

%N Numbers whose cyclic permutations are pairwise coprime.

%C No term, except 10, contains a '0' digit.

%C No term contains two even digits.

%C No term > 9 is a multiple of 3.

%C No term contains two '5' digits.

%C This sequence contains A287198.

%C This sequence does not contain any term > 9 of A084433.

%C In the scatterplot of the first 10000 terms:

%C - the jump from a(7128) = 99998 to a(7129) = 111112 is due to the fact that there is no term > 10 starting with "10",

%C - 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,

%C - these features can be seen at different scales (see scatterplots in Links section).

%H Rémy Sigrist, <a href="/A287513/b287513.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A287513/a287513.png">Scatterplot of the first 2000 terms</a>

%H Rémy Sigrist, <a href="/A287513/a287513_1.png">Scatterplot of the first 10000 terms</a>

%H Rémy Sigrist, <a href="/A287513/a287513_2.png">Scatterplot of the first 150000 terms</a>

%e The cyclic permutations of 5992 are:

%e - 5992 = 2^3 * 7 * 107

%e - 9925 = 5^2 * 397

%e - 9259 = 47 * 197

%e - 2599 = 23 * 113.

%e These values are pairwise coprime, hence 5992 appear in the sequence.

%e The cyclic permutations of 5776 are:

%e - 5776 = 2^4 * 19^2,

%e - 7765 = 5 * 1553,

%e - 7657 = 13 * 19 * 31,

%e - 6577 = 6577.

%e gcd(5776, 7657) = 19, hence 5776 does not appear in the sequence.

%o (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)

%Y Cf. A084433, A287198.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, May 26 2017