A330531 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by 6.

1, 6, 2, 3, 4, 9, 8, 12, 5, 18, 7, 24, 10, 15, 14, 21, 16, 27, 20, 30, 11, 36, 13, 42, 17, 48, 19, 54, 22, 33, 26, 39, 28, 45, 32, 51, 34, 57, 38, 60, 23, 66, 25, 72, 29, 78, 31, 84, 35, 90, 37, 96, 40, 63, 44, 69, 46, 75, 50, 81, 52, 87, 56, 93, 58, 99, 62

Offset: 1

Author

Rémy Sigrist, Dec 17 2019

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers with inverse A330577.

Apparently:

- for m > 1, the m-th run of consecutive terms such that gcd(6, a(n)) = 1 or 6 has 4*m-3 terms,

- for m > 1, the m-th run of consecutive terms such that gcd(6, a(n)) = 2 or 3 has 4*m-1 terms.

Examples

			The first terms, alongside their product with the next term, are:
  n   a(n)  a(n)*a(n+1)
  --  ----  -----------
   1     1            6
   2     6           12
   3     2            6
   4     3           12
   5     4           36
   6     9           72
   7     8           96
   8    12           60
   9     5           90
  10    18          126
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 10000 terms
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A330530 for a similar sequence and additional comments.

Cf. A330577 (inverse).

Programs

PARI

s=0; v=1; for (n=1, 10 000, print (n " " v); s+=2^v; for (w=1, oo, if (!bittest(s,w) && (v*w)%6==0, v=w; break)))