A368103 a(1)=1; for n>1, a(n) is the smallest number not already used which has a factor difference in common with a(n-1).

1, 4, 9, 16, 7, 27, 40, 10, 18, 8, 3, 15, 24, 6, 2, 12, 5, 21, 32, 45, 13, 28, 54, 26, 42, 20, 30, 14, 36, 17, 57, 80, 35, 48, 23, 75, 11, 39, 56, 72, 22, 46, 94, 144, 19, 63, 88, 43, 135, 55, 91, 112, 25, 49, 64, 31, 99, 120, 38, 60, 29, 93, 128, 33, 65, 84, 41, 129, 176, 50, 66, 92, 141, 192

Offset

1,2

Comments

A factor difference of x is any abs(p-q) where x=p*q (in other words, the difference of a factor pair of x, per A368312).

Prime numbers are among the numbers which appear most delayed in this sequence. - Thomas Scheuerle, Dec 12 2023

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Thomas Scheuerle, MATLAB Script.

Thomas Scheuerle, Plot of the first 393 prime numbers over their indices of appearance. It is remarkable that prime numbers do not appear in order.

Example

For n=2, a(1)=1 can be factored only as 1*1, which has difference 0. The next term cannot be 2 and 3 as they do not have a factor difference 0, but 4 = 2*2 does, so that a(2) = 4.
For n=5, a(4)=16 has factor differences 0,6,15 and the smallest unused number with one of those differences is a(5) = 7 = 7*1 difference 6.

Prog

(MATLAB) See link. - Thomas Scheuerle, Dec 12 2023

Crossrefs

Cf. A368312.

Cf. A368059 (with factor sums), A359035, A360995.

Sequence in context: A096879 A070441 A070440 * A054580 A165488 A366862

Adjacent sequences: A368100 A368101 A368102 * A368104 A368105 A368106

Keyword

nonn

Author

Neal Gersh Tolunsky, Dec 11 2023

Status

approved