A387080 a(1)=1, a(2)=3; thereafter a(n) is either the greatest number k < a(n-1) not already used such that gcd(k, a(n-1)) > 1, or if no such k exists then a(n) is the smallest number k > a(n-1) not already used such that gcd(k, a(n-1)) > 1.
1, 3, 6, 4, 2, 8, 10, 5, 15, 12, 9, 18, 16, 14, 7, 21, 24, 22, 20, 25, 30, 28, 26, 13, 39, 36, 34, 32, 38, 19, 57, 54, 52, 50, 48, 46, 44, 42, 40, 35, 45, 33, 27, 51, 17, 68, 66, 64, 62, 60, 58, 56, 49, 63, 69, 23, 92, 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70
Offset: 1
Keywords
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.
- Michael De Vlieger, Log log scatterplot of a(n) in red and A386482(n) in blue, n = 1..2^20.
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16, showing primes in red, proper prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and purple, where the latter represents powerful numbers that are not prime powers.
Crossrefs
Cf. A386482.
Programs
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Mathematica
Block[{c, j, k, m, p, r, nn}, nn = 2^12; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 1; {1}~Join~Monitor[Most@ Reap[Do[ If[PrimePowerQ[j], Set[{p, k, m}, {#1, #1^(#2 - 1), #1^(#2 - 1)}] & @@ FactorInteger[j][[1]]; While[And[c[k*p], k != 0], k--]; If[k == 0, k = m; While[c[k*p], k++]]; k *= p, k = j - 1; While[And[Or[c[k], CoprimeQ[j, k]], k != 1], k--]; If[k == 1, k += j; While[Or[c[k], CoprimeQ[j, k] ], k++] ] ]; If[Mod[j, 2] == Mod[k, 2], r++, Sow[r]; r = 1]; Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]
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