A112975 Lexicographically earliest permutation of the natural numbers such that each term has a common divisor with at least two earlier terms, a(n)=n for n<4.

1, 2, 3, 6, 4, 8, 9, 10, 12, 14, 15, 5, 16, 18, 20, 21, 7, 22, 24, 25, 26, 27, 28, 30, 32, 33, 11, 34, 35, 36, 38, 39, 13, 40, 42, 44, 45, 46, 48, 49, 50, 51, 17, 52, 54, 55, 56, 57, 19, 58, 60, 62, 63, 64, 65, 66, 68, 69, 23, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86

Offset

1,2

Comments

Inverse: A112978; A112977(n) = a(a(n));

For n>3: n is prime iff a(n) < a(n-1); a(A112976(n)) = A000040(n).

For n>8, a(n) can be described as follows: all composite numbers in natural order, with primes inserted so that every prime p immediately follows 3p. - Ivan Neretin, Apr 26 2015

Links

Ivan Neretin, Table of n, a(n) for n = 1..1000

Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A089088.

Sequence in context: A132169 A273666 A302023 * A257218 A349702 A289055

Adjacent sequences: A112972 A112973 A112974 * A112976 A112977 A112978

Keyword

nonn

Author

Reinhard Zumkeller, Oct 08 2005

Status

approved