A285039 Lexicographically earliest sequence of distinct terms such that, for any n>0, a(n) is divisible by k and a(n+1) is divisible by prime(k) for some k.

1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 13, 14, 15, 11, 16, 18, 20, 21, 17, 22, 24, 19, 26, 27, 23, 28, 30, 25, 32, 33, 31, 34, 36, 35, 38, 39, 40, 29, 42, 43, 44, 45, 46, 48, 37, 50, 51, 52, 41, 54, 55, 56, 49, 58, 57, 60, 47, 62, 63, 64, 53, 66, 65, 68, 59, 70

Offset

1,2

Comments

As prime(1)=2, this sequence can always be extended with an even number.

This sequence is a permutation of the natural numbers, with inverse A285041 (say prime(k) divides n: the sequence contains all the multiples of 2*k, hence n will eventually be chosen).

This sequence has a fractal structure that is highlighted in the illustrations of some derived sequences in the Links section.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of a(n)-n

Rémy Sigrist, Scatterplot of Sum_{k=1..n} (-1)^a(n)

Rémy Sigrist, PARI program for A285039

Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A285041 (inverse).

Sequence in context: A335430 A121878 A167905 * A260307 A285041 A265734

Adjacent sequences: A285036 A285037 A285038 * A285040 A285041 A285042

Keyword

nonn

Author

Rémy Sigrist, Apr 08 2017

Status

approved