A359256 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared such that all the distinct prime factors of a(n-1) + a(n) are factors of a(n).

1, 2, 6, 3, 24, 8, 56, 42, 7, 336, 48, 16, 112, 84, 12, 4, 28, 21, 60, 15, 10, 22, 66, 30, 18, 9, 72, 36, 45, 80, 20, 5, 120, 40, 85, 204, 39, 78, 26, 38, 90, 35, 14, 50, 75, 150, 93, 186, 57, 114, 102, 34, 94, 162, 54, 27, 216, 108, 135, 240, 144, 99, 198, 44, 77, 266, 95, 380, 132, 110, 11

Offset

1,2

Comments

The primes do not occur in their natural order, and for all terms studied if a(n) is a prime p, then a(n-1) = p(p-1) and a(n+1) = p(p^2-1). In the first 10000 terms the fixed points are 22, 165, 710, 1005, 9003, although it is likely more exist. The sequence is conjectured to be a permutation of the positive integers.

Links

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

Example

a(3) = 6 as a(2) + 6 = 2 + 6 = 8 which has 2 as its only distinct prime factor, and 2 is a factor of 6.
a(8) = 42 as a(7) + 42 = 56 + 42 = 96 which has 2 and 3 as distinct prime factors,  and 2 and 3 are factors of 42.
a(10) = 336 as a(9) + 336 = 7 + 336 = 343 which has 7 as its only distinct prime factor, and 7 is a factor of 336. Note that 336 = 7(7^2-1).

Crossrefs

Cf. A359557, A027748, A359356, A064413, A352867.

Sequence in context: A178667 A281881 A206493 * A304085 A302783 A364318

Adjacent sequences: A359253 A359254 A359255 * A359257 A359258 A359259

Keyword

nonn

Author

Scott R. Shannon and Eric Angelini, Jan 05 2023

Status

approved