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

1,2

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.

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

Example

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

Prog

(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)))

Crossrefs

See A330530 for a similar sequence and additional comments.

Cf. A330577 (inverse).

Sequence in context: A094775 A362922 A019662 * A374645 A134105 A167509

Adjacent sequences: A330528 A330529 A330530 * A330532 A330533 A330534

Keyword

nonn

Author

Rémy Sigrist, Dec 17 2019

Status

approved