A287513 Numbers whose cyclic permutations are pairwise coprime.

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

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

Cf. A084433, A287198.

Sequence in context: A050724 A336813 A209860 * A194403 A305707 A161979

Adjacent sequences: A287510 A287511 A287512 * A287514 A287515 A287516

Keyword

nonn,base

Author

Rémy Sigrist, May 26 2017

Status

approved