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A353075 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that shares a factor with a(n-1) * a(n-2) + |a(n-1) - a(n-2)|. 1
1, 2, 3, 7, 5, 37, 14, 541, 8101, 223, 23, 73, 13, 1009, 11, 12097, 46, 22, 4, 6, 8, 10, 12, 16, 18, 15, 9, 21, 24, 26, 20, 28, 30, 32, 34, 25, 859, 35, 17, 613, 69, 42841, 39, 1713601, 19, 92, 27, 2549, 38, 43, 33, 1429, 115, 44, 42, 36, 40, 48, 50, 52, 54, 45, 51, 57, 60, 49, 65, 55, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The sequence produces numerous groupings of primes. For example a(3) to a(16) contains thirteen primes in fourteen terms, a(80) to a(102) contains fourteen primes in twenty-three terms. The sequences is conjectured to be a permutation of the positive integers.
LINKS
Michael De Vlieger, Log-log scatterplot of a(n), n = 1..5000, showing primes in red.
EXAMPLE
a(5) = 5 as a(4)*a(3)+|a(4)-a(3)| = 7*3+|7-3| = 25, and 5 is the smallest unused number that shares a factor with 25.
MATHEMATICA
nn = 69; c[_] = 0; a[1] = c[1] = 1; a[2] = c[2] = 2; u = 3; Do[m = #1 #2 + Abs[#2 - #1] & @@ {a[i - 2], a[i - 1]}; If[PrimeQ[m], k = 1; While[c[k m] != 0, k++]; k = k m, k = u; While[Nand[c[k] == 0, ! CoprimeQ[m, k]], k++]]; Set[{a[i], c[k]}, {k, i}]; If[a[i] == u, While[c[u] > 0, u++]], {i, 3, nn}]; Array[a, nn] (* Michael De Vlieger, May 02 2022 *)
CROSSREFS
Sequence in context: A063696 A258126 A332211 * A069587 A059843 A092927
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 22 2022
STATUS
approved

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Last modified July 17 12:22 EDT 2024. Contains 374377 sequences. (Running on oeis4.)