A365059 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).

2, 4, 6, 5, 10, 7, 14, 9, 3, 12, 15, 8, 16, 18, 20, 21, 30, 40, 28, 27, 24, 25, 35, 36, 45, 32, 22, 13, 26, 60, 50, 42, 48, 55, 64, 34, 19, 38, 63, 70, 56, 54, 65, 72, 75, 80, 49, 77, 90, 100, 84, 96, 85, 44, 39, 112, 81, 33, 98, 99, 126, 108, 95, 120, 110, 144, 105, 135, 88, 52, 150, 130, 140

Offset

1,1

Comments

In the first 500000 terms the only fixed points are 38 and 209, although it is likely more exist. In the same range the smallest missing numbers are 311, 313, 337. The sequence is conjectured to be a permutation of the integers >= 2.

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(3) = 6 as a(2) = 4 and A008472(4) = 2, and 6 is the smallest unused number that is a multiple of 2.
a(11) = 15 as a(10) = 12 and A008472(12) = 5, and 15 is the smallest unused number that is a multiple of 5.

Crossrefs

Cf. A008472, A365060, A300813.

Sequence in context: A367711 A365060 A376548 * A083718 A319804 A055948

Adjacent sequences: A365056 A365057 A365058 * A365060 A365061 A365062

Keyword

nonn

Author

Scott R. Shannon, Aug 19 2023

Status

approved