cp's OEIS Frontend

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.

A285549 Smallest weak pseudoprime to all natural bases up to prime(n) that is not a Carmichael number.

This page as a plain text file.
%I A285549 #41 Nov 14 2022 05:57:27
%S A285549 341,2701,721801,721801,42702661,1112103541,2380603501,5202153001,
%T A285549 17231383261,251994268081,1729579597021,55181730338101,
%U A285549 142621888086541,242017633321201,242017633321201,242017633321201,1174858593838021,1174858593838021,168562580058457201,790489610041255741,790489610041255741,790489610041255741
%N A285549 Smallest weak pseudoprime to all natural bases up to prime(n) that is not a Carmichael number.
%C A285549 a(n) is the smallest composite k such that p^k == p (mod k) for every prime p <= A000040(n) and A002322(k) does not divide k-1.
%C A285549 If a composite m < a(n) and p^m == p (mod m) for every prime p <= prime(n), then m is a Carmichael number.
%C A285549 a(23) > 2^64. - _Max Alekseyev_, Apr 22 2017
%C A285549 Conjecture: lpf(a(n)) > prime(n), where lpf = A020639. - _Thomas Ordowski_, May 13 2017
%C A285549 Except a(19), the listed terms are semiprime. - _Thomas Ordowski_, Feb 09 2018
%C A285549 a(24) <= 21150412877533909683421, a(362) <= (416*A002110(360) + 1) * (832*A002110(360) + 1). - _Daniel Suteu_, Nov 13 2022
%Y A285549 Cf. A002997, A020639, A083876, A285512.
%K A285549 nonn
%O A285549 1,1
%A A285549 _Thomas Ordowski_, Apr 21 2017
%E A285549 a(5)-a(9) from _Giovanni Resta_, Apr 21 2017
%E A285549 a(10)-a(22) from _Max Alekseyev_, Apr 22 2017