cp's OEIS Frontend

A265669 Carmichael numbers that are the average of two consecutive primes.

%I A265669 #22 Feb 16 2025 08:33:27
%S A265669 15841,126217,656601,1193221,2704801,6189121,8134561,8719921,11205601,
%T A265669 13992265,40917241,41298985,43286881,56052361,76595761,88689601,
%U A265669 105869401,130497361,167979421,175997185,186782401,289766701,367939585,597717121,633639097
%N A265669 Carmichael numbers that are the average of two consecutive primes.
%C A265669 Motivation was the form of differences between consecutive primes that generate this sequence. It seems that 12*k appears in all differences except 4.
%C A265669 Differences between corresponding consecutive primes are 36, 12, 4, 24, 24, 24, 24, 36, 24, 12, 36, 12, 36, 36, 60, 24, 36, 36, 60, 36, 24, 24, 24, 36, 12, 24 ...
%H A265669 Amiram Eldar, <a href="/A265669/b265669.txt">Table of n, a(n) for n = 1..10000</a>
%H A265669 G. Tarry, I. Franel, A. Korselt, and G. Vacca, <a href="https://oeis.org/wiki/File:Probl%C3%A8me_chinois.pdf">Problème chinois</a>, L'intermédiaire des mathématiciens 6 (1899), pp. 142-144.
%H A265669 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>
%H A265669 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>
%e A265669 15841 is a term because it is a Carmichael number and average of 15823 and 15859 that are consecutive primes is equal to 15841.
%e A265669 126217 is a term because it is a Carmichael number and average of 126211 and 126223 that are consecutive primes is equal to 126217.
%o A265669 (PARI) is(n)={my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1}
%o A265669 forcomposite(n=1, 1e9, if(is(n) && (nextprime(n)-n)==(n-precprime(n)), print1(n,", ")))
%Y A265669 Cf. A002997.
%K A265669 nonn
%O A265669 1,1
%A A265669 _Altug Alkan_, Dec 12 2015