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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, Table of n, a(n) for n = 1..5000 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 Cf. A353006, A353082, A352867, A352774, A352768. Sequence in context: A063696 A258126 A332211 * A069587 A059843 A092927 Adjacent sequences: A353072 A353073 A353074 * A353076 A353077 A353078 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.)