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 A212843 #11 Feb 16 2025 08:33:17 %S A212843 252601,399001,512461,852841,1193221,1857241,1909001,2100901,3828001, %T A212843 5049001,5148001,5481451,6189121,7519441,8341201,9439201,10024561, %U A212843 10837321,14676481,15247621,17236801,27062101,29111881,31405501,33302401,34657141,40430401,42490801 %N A212843 Carmichael numbers that have only prime divisors of the form 10k+1. %C A212843 Conjecture: only Carmichael numbers of the form 10n+1 can have prime divisors of the form 10k+1 (but not all Carmichael numbers of the form 10n+1 have prime divisors of the form 10k+1). %C A212843 Checked up to Carmichael number 4954039956700380001. %C A212843 Conjecture: all Carmichael numbers C (not only with three prime divisors) of the form 10n+1 that have only prime divisors of the form 10k+1 can be written as C = (30a+1)*(30b+1)*(30c+1), C = (30a+11)*(30b+11)*(30c+11), or C = (30a+1)*(30b+11)*(30c+11). In other words, there are no numbers of the form C = (30a+1)*(30b+1)*(30c+11). %C A212843 Checked for all Carmichael numbers from the sequence above. %C A212843 The first conjecture is a consequence of Korselt's criterion. - _Charles R Greathouse IV_, Oct 02 2012 %H A212843 Charles R Greathouse IV, <a href="/A212843/b212843.txt">Table of n, a(n) for n = 1..10000</a> %H A212843 E. W. Weisstein, <a href="https://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a> %Y A212843 Subsequence of A004615. %K A212843 nonn %O A212843 1,1 %A A212843 _Marius Coman_, May 28 2012 %E A212843 Terms corrected by _Charles R Greathouse IV_, Oct 02 2012