This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343815 #26 May 16 2021 01:48:38
%S A343815 1,3,7,23,199,2297,3473,124311,262193,580011,2847499,16329689,
%T A343815 115495383,399128719,13657103441,16022594389,66275713667,733100630963,
%U A343815 1291428223783,5340370800707
%N A343815 Cyclic numbers (A003277) which set a record for the gap to the next cyclic number.
%C A343815 Since the asymptotic density of the cyclic numbers is 0 (Erdős, 1948), this sequence is infinite.
%C A343815 The corresponding record values are 1, 2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 40, 42, ...
%H A343815 Paul Erdős, <a href="http://www.renyi.hu/~p_erdos/1948-11.pdf">Some asymptotic formulas in number theory</a>, J. Indian Math. Soc. (N.S.), Vol. 12 (1948), pp. 75-78.
%e A343815 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.
%e A343815 From _Martin Ehrenstein_, May 11 2021: (Start)
%e A343815 Table of the first 4 terms:
%e A343815 n | cyclic number | gap
%e A343815 ---+---------------+----
%e A343815 1 | 1 | 1
%e A343815 | 2 | 1
%e A343815 2 | 3 | 2
%e A343815 | 5 | 2
%e A343815 3 | 7 | 4
%e A343815 | 11 | 2
%e A343815 | 13 | 2
%e A343815 | 15 | 2
%e A343815 | 17 | 2
%e A343815 | 19 | 4
%e A343815 4 | 23 | 6
%e A343815 | 29 | ...
%e A343815 ...| ... | ...
%e A343815 (End)
%t A343815 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
%Y A343815 Cf. A003277, A343816.
%K A343815 nonn,more
%O A343815 1,2
%A A343815 _Amiram Eldar_, Apr 30 2021
%E A343815 a(18)-a(20) from _Martin Ehrenstein_, May 15 2021