cp's OEIS Frontend

A270267 Carmichael numbers (A002997) that are the sum of three consecutive primes.

%I A270267 #26 Jun 25 2019 11:55:44
%S A270267 252601,410041,1615681,2113921,10606681,10877581,11921001,26932081,
%T A270267 44238481,54767881,82929001,120981601,128697361,208969201,246446929,
%U A270267 255160621,278152381,280067761,311388337,325546585,334783585,416964241,533860309,593234929,672389641
%N A270267 Carmichael numbers (A002997) that are the sum of three consecutive primes.
%C A270267 In other words, Carmichael numbers of the form p + q + r where p, q and r are consecutive primes.
%C A270267 If a Carmichael number is the sum of n consecutive primes, it is so obvious that the minimum value of n is 3.
%C A270267 Intersection of A002997 and A034961.
%H A270267 Amiram Eldar, <a href="/A270267/b270267.txt">Table of n, a(n) for n = 1..10000</a>
%e A270267 84191, 84199 and 84211 are consecutive primes and sum of them is 252601 that is a Carmichael number.
%e A270267 136657, 136691 and 136693 are consecutive primes and sum of them is 410041 that is a Carmichael number.
%e A270267 538553, 538561 and 538567 are consecutive primes and sum of them is 1615681 that is a Carmichael number.
%o A270267 (PARI) isA002997(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 A270267 a034961(n) = my(p=prime(n), q=nextprime(p+1)); p+q+nextprime(q+1);
%o A270267 for(n=1, 1e6, if(isA002997(a034961(n)), print1(a034961(n), ", ")));
%Y A270267 Cf. A002997, A034961.
%K A270267 nonn
%O A270267 1,1
%A A270267 _Altug Alkan_, Mar 14 2016
%E A270267 More terms from _Amiram Eldar_, Jun 25 2019