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 A358978 Numbers that are coprime to the number of terms in their Zeckendorf representation (A007895). 4
 1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 20, 21, 23, 25, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 47, 49, 50, 51, 52, 53, 55, 57, 59, 61, 62, 63, 64, 65, 67, 70, 71, 73, 75, 77, 79, 83, 85, 87, 88, 89, 91, 95, 97, 98, 100, 101, 103, 104, 107, 109 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A063743 at n = 22. Numbers k such that gcd(k, A007895(k)) = 1. The Fibonacci numbers (A000045) are terms. These are also the only Zeckendorf-Niven numbers (A328208) in this sequence. Includes all the prime numbers. The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 61, 614, 6028, 61226, 606367, 6041106, 61235023, 612542436, 6034626175, 60093287082, 609082612171, ... . Conjecture: The asymptotic density of this sequence exists and equals 6/Pi^2 = 0.607927... (A059956), the same as the density of A094387. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 3 is a term since A007895(3) = 1, and gcd(3, 1) = 1. MATHEMATICA z[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; Select[Range[120], CoprimeQ[#, z[#]] &] (* after Alonso del Arte at A007895 *) PROG (PARI) is(n) = if(n<4, 1, my(k=2, m=n, s, t); while(fibonacci(k++)<=m, ); while(k && m, t=fibonacci(k); if(t<=m, m-=t; s++); k--); gcd(n, s)==1); \\ after Charles R Greathouse IV at A007895 CROSSREFS Cf. A007895, A059956, A063743, A328208. Subsequences: A000040, A000045. Similar sequences: A094387, A339076, A358975, A358976, A358977. Sequence in context: A256133 A078643 A137698 * A063743 A353968 A144100 Adjacent sequences: A358975 A358976 A358977 * A358979 A358980 A358981 KEYWORD nonn,base AUTHOR Amiram Eldar, Dec 07 2022 STATUS approved

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Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)