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

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

Offset: 1

Author

Altug Alkan, Mar 14 2016

Keywords

• nonn

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.

Intersection of A002997 and A034961.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002997, A034961.

Programs

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), ", ")));

Extensions

More terms from Amiram Eldar, Jun 25 2019