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A337136 a(0) = 0, a(1) = 1; for n > 1, a(n) = smallest positive number which has not appeared which has a common factor with a(n-2)+a(n-1). 1
0, 1, 2, 3, 5, 4, 6, 8, 7, 9, 10, 19, 29, 12, 41, 53, 14, 67, 15, 16, 31, 47, 13, 18, 62, 20, 22, 21, 43, 24, 134, 26, 25, 17, 27, 11, 28, 30, 32, 34, 33, 201, 36, 39, 35, 37, 38, 40, 42, 44, 46, 45, 49, 48, 97, 50, 51, 101, 52, 54, 56, 55, 57, 58, 23, 60, 83, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is a permutation of the natural numbers. Up to 1 million terms the fixed points are 0,1,2,3,6,9,10, and it is likely these are the only terms.

LINKS

Table of n, a(n) for n=0..67.

Scott R. Shannon, Image of the first 1000000 terms. The green line is y=x.

EXAMPLE

a(5) = 4 as a(3)+a(4) = 3+5 = 8, and 4 is the smallest number that shares a common factor with 8 that has not yet appeared.

a(11) = 19 as a(9)+a(10) = 9+10 = 19, and as 19 is prime, a(11) must be the smallest multiple of 19 that has not yet appeared, being 19 in this case.

CROSSREFS

Cf. A064413, A336957, A098550, A089088, A251622.

Sequence in context: A233278 A075168 A075169 * A138606 A166013 A089864

Adjacent sequences:  A337133 A337134 A337135 * A337137 A337138 A337139

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Aug 18 2020

STATUS

approved

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Last modified October 23 13:32 EDT 2021. Contains 348214 sequences. (Running on oeis4.)