A343815 Cyclic numbers (A003277) which set a record for the gap to the next cyclic number.
1, 3, 7, 23, 199, 2297, 3473, 124311, 262193, 580011, 2847499, 16329689, 115495383, 399128719, 13657103441, 16022594389, 66275713667, 733100630963, 1291428223783, 5340370800707
Offset: 1
Examples
The first 6 cyclic numbers are 1, 2, 3, 5, 7 and 11. The gaps between them are 1, 1, 2, 2 and 4. The record gaps, 1, 2 and 4, occur after the cyclic numbers 1, 3 and 7, which are the first 3 terms of this sequence.
From _Martin Ehrenstein_, May 11 2021: (Start)
Table of the first 4 terms:
n | cyclic number | gap
---+---------------+----
1 | 1 | 1
| 2 | 1
2 | 3 | 2
| 5 | 2
3 | 7 | 4
| 11 | 2
| 13 | 2
| 15 | 2
| 17 | 2
| 19 | 4
4 | 23 | 6
| 29 | ...
...| ... | ...
(End)
Links
- Paul Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. (N.S.), Vol. 12 (1948), pp. 75-78.
Programs
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Mathematica
cycQ[n_] := CoprimeQ[n, EulerPhi[n]]; seq = {}; m = 1; dm = 0; Do[If[cycQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 2, 10^6}]; seq
Extensions
a(18)-a(20) from Martin Ehrenstein, May 15 2021
Comments