A330577 -id:A330577 - cp's OEIS frontend

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

Rémy Sigrist, Dec 17 2019

nonn

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.

			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

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

See A330530 for a similar sequence and additional comments.

Cf. A330577 (inverse).

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)))

cp's OEIS Frontend

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

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