

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(n1) * a(n2) + a(n1)  a(n2).


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
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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 twentythree terms. The sequences is conjectured to be a permutation of the positive integers.


LINKS



EXAMPLE

a(5) = 5 as a(4)*a(3)+a(4)a(3) = 7*3+73 = 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



KEYWORD

nonn


AUTHOR



STATUS

approved



