

A270267


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


2



252601, 410041, 1615681, 2113921, 10606681, 10877581, 11921001, 26932081, 44238481, 54767881, 82929001, 120981601, 128697361, 208969201, 246446929, 255160621, 278152381, 280067761, 311388337, 325546585, 334783585, 416964241, 533860309, 593234929, 672389641
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

In other words, Carmichael numbers of the form p + q + r where p, q and r are consecutive primes.
If a Carmichael number is the sum of n consecutive primes, it is so obvious that the minimum value of n is 3.


LINKS



EXAMPLE

84191, 84199 and 84211 are consecutive primes and sum of them is 252601 that is a Carmichael number.
136657, 136691 and 136693 are consecutive primes and sum of them is 410041 that is a Carmichael number.
538553, 538561 and 538567 are consecutive primes and sum of them is 1615681 that is a Carmichael number.


PROG

(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}
a034961(n) = my(p=prime(n), q=nextprime(p+1)); p+q+nextprime(q+1);
for(n=1, 1e6, if(isA002997(a034961(n)), print1(a034961(n), ", ")));


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



