A330576 -id:A330576 - cp's OEIS frontend

A330530 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by 4.

1, 4, 2, 6, 8, 3, 12, 5, 16, 7, 20, 9, 24, 10, 14, 18, 22, 26, 28, 11, 32, 13, 36, 15, 40, 17, 44, 19, 48, 21, 52, 23, 56, 25, 60, 27, 64, 29, 68, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 72, 31, 76, 33, 80, 35, 84, 37, 88, 39, 92, 41, 96, 43, 100, 45, 104

Offset: 1

Rémy Sigrist, Dec 17 2019

For any k > 0, let f_k be the lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by k:
- in particular:
     f_1 = f_2 = A000027,
     f_3 = A006368,
     f_4 = a (this sequence),
     f_6 = A330531,
- f_k is a permutation of the natural numbers,
- f_k(1) = 1, f_k(2) = max(2, k),
- if k is prime, then f_k corresponds to the integers that are not multiple of k interspersed with the integers that are multiple of k.
Apparently:
- for m > 0, the m-th run of consecutive terms such that gcd(a(n), 4) = 2 has A153893(m+1) terms,
- for m > 1, the m-th run of consecutive terms such that gcd(a(n), 4) = 1 or 4 has A068156(m+1) terms.

			The first terms, alongside their product with the next term, are:
  n   a(n)  a(n)*a(n+1)
  --  ----  -----------
   1     1            4
   2     4            8
   3     2           12
   4     6           48
   5     8           24
   6     3           36
   7    12           60
   8     5           80
   9    16          112
  10     7          140

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

Cf. A006368, A068156, A153893, A330531 (f_6), A330576 (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)%4==0, v=w; break)))

cp's OEIS Frontend

A330530 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by 4.

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