A368103 -id:A368103 - cp's OEIS frontend

A368059 a(1)=3; for n>1, a(n) is the smallest positive integer not already used which has a factor sum in common with a(n-1).

3, 4, 6, 10, 12, 7, 15, 16, 9, 5, 8, 14, 18, 20, 11, 27, 32, 17, 45, 13, 24, 21, 25, 48, 28, 30, 22, 36, 19, 51, 64, 33, 40, 42, 52, 60, 31, 87, 112, 57, 72, 26, 44, 23, 63, 39, 55, 108, 38, 54, 50, 56, 29, 81, 65, 77, 80, 41, 117, 85, 96, 34, 66, 46, 84, 43, 123, 160, 69, 88, 70, 78, 90, 62

Offset: 1

Neal Gersh Tolunsky, Dec 17 2023

nonn

A factor sum of x is any p+q where x=p*q, those sums being row x of A335572.
Is this an infinite sequence?
When every product of two integers with sum s has appeared in the sequence, that sum s is no longer a potential link between a(n) and a(n-1). If a number appears whose factor sums have all been exhausted, the sequence ends.

			For n=2, 3 can only be factored as 1*3, which has a sum of 4. The next term cannot be 1 or 2 as they do not have a factor sum of 4, but 4 = 2*2 does, so a(2) = 4.
For n=5, a(4)=10 has factor sums 7 and 11. The smallest unused number with one of those sums is a(5) = 12 = 3*4, sum of 7.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Thomas Scheuerle, MATLAB Program.
Thomas Scheuerle, Histogram of a(n)/n for the first 5000 values of this sequence.

Cf. A335572 (factor sums).

Cf. A368103 (with factor differences).

MATLAB
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% See Scheuerle link.
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cp's OEIS Frontend

A368059 a(1)=3; for n>1, a(n) is the smallest positive integer not already used which has a factor sum in common with a(n-1).

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