A358277 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) is coprime to the previous Omega(a(n-1)) terms.
1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 13, 12, 17, 14, 15, 19, 16, 23, 18, 25, 29, 20, 21, 31, 22, 27, 35, 26, 33, 37, 24, 41, 28, 43, 30, 47, 32, 53, 34, 39, 49, 38, 45, 59, 36, 61, 40, 67, 42, 71, 44, 65, 51, 46, 55, 57, 52, 73, 48, 79, 50, 77, 69, 58, 83, 54, 85, 89, 56, 97, 60, 101, 62, 63, 95
Offset: 1
Keywords
Examples
a(4) = 4 as a(3) = 3 and Omega(3) = A001222(3) = 1, and 4 is coprime to the previous one term, namely a(3) = 3. a(9) = 11 as a(8) = 8 and Omega(8) = A001222(8) = 3, and 11 is coprime to the previous three terms, namely 8, 7, 6.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..16384
- Michael De Vlieger, Log log scatterplot of a(n) n = 1..2^10, with records in red, local minima in blue, highlighting primes in green and other prime powers in gold, showing numbers that are neither squarefree nor prime powers in magenta.
- Michael De Vlieger, Scalar scatterplot of a(n), n = 1..2^12, showing primes in red, composite prime powers in gold, composite squarefree numbers in green, products of composite prime powers in magenta, and other numbers in blue.
- Michael De Vlieger, Log-log scatterplot of a(n), n = 1..2^10 using a color function showing Omega(a(n-1)).
Programs
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Mathematica
nn = 90; c[] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = 3; j = 2; Do[k = u; m = Times @@ Array[a[n - #] &, PrimeOmega[j]]; While[Nand[! c[k], CoprimeQ[k, m]], k++]; Set[{a[n], c[k], j}, {k, True, k}]; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* _Michael De Vlieger, Nov 20 2022 *)
Comments