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 A110358 #23 Feb 27 2020 22:31:45
%S A110358 3,5,7,17,19,23,37,53,59,61,71,73,97,107,109,113,163,179,181,257,293,
%T A110358 307,347,349,359,367,373,401,439,487,491,499,547,557,631,751,773,797,
%U A110358 853,881,883,887,907,971,1009,1039,1049,1051,1097,1103,1123,1283,1297
%N A110358 Beginning with 3, the least prime which is the product of one or more previous terms + 2.
%C A110358 Conjecture: The sequence is infinite.
%C A110358 Subbarao & Yip prove that if there is an integer m such that the equation Phi_2(x) = m has a unique solution, where Phi_2 is the 2nd Schemmel totient function (A058026), then x == 0 (mod a(n)^2) for each term in this sequence. They conjectured an analog to Carmichael's conjecture, that this equation has no unique solution to any integer m, and prove that any counterexample to this conjecture is > 10^120000, a bound calculated from the first 10000 terms of this sequence. A proof that this sequence is infinite would prove the conjecture. - _Amiram Eldar_, Mar 25 2017
%H A110358 Giovanni Resta, <a href="/A110358/b110358.txt">Table of n, a(n) for n = 1..10000</a>
%H A110358 M. V. Subbarao and L. W. Yip, <a href="http://www.math.ualberta.ca/~subbarao/documents/Subbarao_Yip1989.pdf">Carmichael's conjecture and some analogues</a>, Théorie des nombres/Number Theory: Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987, Jean M. de Koninck and Claude Levesque, eds., Walter de Gruyter, 1989, pp. 928-941.
%e A110358 After 3, 5 and 7 the next term is 3*5 + 2 = 17, then 17 + 2 = 19, then 3*7 + 2 = 23, then 5*7 + 2 = 37, etc.
%t A110358 L={3}; p=3; While[Length[L] < 100, p = NextPrime@p; If[SquareFreeQ[p - 2] && SubsetQ[L, First /@ FactorInteger[p - 2]], AppendTo[L, p]]]; L (* _Giovanni Resta_, Mar 25 2017 *)
%Y A110358 Cf. A058026.
%K A110358 nonn
%O A110358 1,1
%A A110358 _Amarnath Murthy_, Jul 23 2005
%E A110358 More terms from John Pammer (jcp5027(AT)psu.edu), Oct 10 2005
%E A110358 Corrected and extended by _Joshua Zucker_, May 08 2006