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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).
2
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
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
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Dec 11 2023
STATUS
approved