A363504 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of prime(Omega(a(n-1))).

1, 2, 4, 3, 6, 9, 12, 5, 8, 10, 15, 18, 20, 25, 21, 24, 7, 14, 27, 30, 35, 33, 36, 28, 40, 42, 45, 50, 55, 39, 48, 11, 16, 49, 51, 54, 56, 63, 60, 70, 65, 57, 66, 75, 80, 22, 69, 72, 44, 85, 78, 90, 77, 81, 84, 91, 87, 93, 96, 13, 26, 99, 95, 102, 100, 98, 105, 110, 115, 108, 88, 112, 121, 111

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers, although it takes many terms for the primes to appear, e.g., a(371221) = 61. After the first two terms the fixed points in the first 500000 terms are 10, 26076, 26151, 26223, 26307, 26379, 26406, although it is possible more exist.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 500000 terms. The green line is a(n) = n.

Example

a(8) = 5 as prime(Omega(a(7))) = prime(A001222(12)) = prime(3) = 5, and 5 is the smallest unused number that is a multiple of 5.

Crossrefs

Cf. A363956, A001222, A000040, A351495.

Sequence in context: A075383 A338919 A348018 * A376905 A332878 A376903

Adjacent sequences: A363501 A363502 A363503 * A363505 A363506 A363507

Keyword

nonn

Author

Scott R. Shannon, Jun 06 2023

Status

approved