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 A387362 #10 Aug 28 2025 10:25:43
%S A387362 1,3,5,11,13,15,17,29,31,33,35,41,51,59,65,67,69,71,77,83,85,87,89,95,
%T A387362 101,107,113,131,137,139,141,143,149,157,159,161,177,179,185,191,197,
%U A387362 209,211,213,215,221,227,233,239,247,249,255,257,263,265,267,269,281,293
%N A387362 Cyclic numbers k such that k+2 is also a cyclic number.
%C A387362 All the lesser members of twin primes (A001359) are terms since every prime is a cyclic number (A003277).
%C A387362 Cohen (2025) conjectured and Pomerance (2025) proved that this sequence is infinite.
%H A387362 Amiram Eldar, <a href="/A387362/b387362.txt">Table of n, a(n) for n = 1..10000</a>
%H A387362 Joel E. Cohen, <a href="https://arxiv.org/abs/2508.08335">Conjectures about Primes and Cyclic Numbers</a>, arXiv:2508.08335 [math.NT], 2025.
%H A387362 Carl Pomerance, <a href="https://math.dartmouth.edu/~carlp/cyclic.pdf">Patterns for cyclic numbers</a>, 2025.
%F A387362 The number of terms <= x is ~ 2 * C_2 * x / (exp(gamma) * log(log(log(x))))^2, where C_2 = A005597, and gamma = A001620 (Pomerance, 2025).
%t A387362 cyclicQ[n_] := cyclicQ[n] = CoprimeQ[n, EulerPhi[n]]; Select[Range[1, 300, 2], And @@ cyclicQ[{#, # + 2}] &]
%o A387362 (PARI) iscyclic(k) = gcd(k, eulerphi(k)) == 1;
%o A387362 isok(k) = k % 2 && iscyclic(k) && iscyclic(k+2);
%Y A387362 Cf. A001620, A005597, A073004, A387363.
%Y A387362 Subsequence of A003277.
%Y A387362 A001359 is a subsequence.
%K A387362 nonn,easy,new
%O A387362 1,2
%A A387362 _Amiram Eldar_, Aug 27 2025