|
%I #19 Oct 15 2023 05:14:27
%S 20543425,80993605,112608685,255063865,307510105,367621765,382017685,
%T 400463665,409631425,430786405,536835565,675787105,950572525,
%U 1040986765,1139137825,1214553025,1404069205,1456119805,1560636805,1608308905,1796972905,1805035225,1823195605
%N Numbers k such that k == 1 (mod 12) and 6*k+1, 12*k+1, 18*k+1, 36*k+1, 72*k+1, 108*k+1 and 144*k+1 are all primes, so N = (6*k+1)*(12*k+1)*(18*k+1), (36*k+1)*N, (72*k+1)*N, (108*k+1)*N and (144*k+1)*N are 5 Carmichael numbers in an arithmetic progression.
%D Andrzej Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad, Yugoslavia, 1972.
%H Amiram Eldar, <a href="/A294031/b294031.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrzej Rotkiewicz, <a href="https://dml.cz/handle/10338.dmlcz/120560">Arithmetic progressions formed by pseudoprimes</a>, Acta Mathematica et Informatica Universitatis Ostraviensis, Vol. 8, No. 1 (2000), pp. 61-74.
%e 20543425 generates 11236306070625187487140801 + 8309959597401596721108558352203300 k which are Carmichael numbers for k = 0 to 4.
%t aQ[n_]:=Mod[n,12]==1 && AllTrue[{6n+1, 12n+1, 18n+1, 36n+1, 72n+1, 108n+1, 144n+1}, PrimeQ]; Select[Range[10^8], aQ]
%Y Cf. A002997.
%Y Subsequence of A017533.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 22 2017
|
