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A351001
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a(0) = 0, a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared which has a common factor with a(n-2) + a(n-1) but does not equal a(n-2) + a(n-1).
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10
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0, 1, 2, 6, 4, 5, 3, 10, 26, 8, 12, 14, 13, 9, 11, 15, 16, 62, 18, 20, 19, 21, 22, 86, 24, 25, 7, 28, 30, 29, 118, 27, 35, 31, 32, 33, 39, 34, 146, 36, 38, 37, 40, 42, 41, 166, 23, 45, 17, 44, 122, 46, 48, 47, 50, 194, 52, 51, 206, 514, 54, 56, 55, 57, 49, 53, 58, 60, 59, 63, 61, 64
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OFFSET
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0,3
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COMMENTS
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This is a permutation of the natural numbers. Up to 500000 terms the fixed points are 0, 1, 2, 4, 5, 15, 16, 18, 21, 22, 24, 25, 29, and it is likely no more exist.
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LINKS
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EXAMPLE
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a(3) = 6 as a(1)+a(2) = 3, 6 does not equal 3, and gcd(3,6) > 1.
a(4) = 4 as a(2)+a(3) = 8, 4 does not equal 8, and gcd(8,4) > 1.
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MATHEMATICA
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s = {0, 1, 2}; u = 3; c[_] = 0; Set[{i, j}, s[[-2 ;; -1]]]; Array[Set[c[s[[#]]], #] &, Length[s]]; s~Join~Reap[Do[Set[k, u]; While[Nand[c[k] == 0, GCD[i + j, k] > 1, i + j != k], k++]; Sow[k]; Set[c[k], n]; If[k == u, While[c[u] == 1, u++]]; i = j; j = k, {n, Length[s] + 1, 2^10}], n]][[-1, -1]] (* Michael De Vlieger, Jan 28 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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