A384191 Unique increasing sequence (a(n)) whose complement, (b(n)), satisfies b(n) = a(a(n))+3.
1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 18, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 40, 41, 42, 46, 47, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 79, 80, 81, 85, 86, 87, 88, 89, 90, 94, 95, 96, 97, 98, 99, 103, 104
Offset: 1
Keywords
Examples
a(a(1)) = a(1) = 1, so b(1) = 4. a(a(2)) = a(2) = 2, so b(2) = 5. a(a(3)) = a(3) = 3, so b(3) = 6. a(a(4)) = a(7) = 10, so b(4) = 13.
Programs
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Mathematica
k = 3; p = k*Array[Floor[#*GoldenRatio] &, 100] ; seq = ConstantArray[1, Last[p]]; seq[[p]] = k + 1; u = Join[{1}, Accumulate[seq] + 1] (* A384191 *) Complement[Range[Last[#]], #] &[u] (* A383192 *) (* Peter J. C. Moses, May 12 2025 *)
Comments