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

1,1

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.

Intersection of A002997 and A034961.

Links

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

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

Cf. A002997, A034961.

Sequence in context: A113567 A083628 A212843 * A255441 A210074 A230484

Adjacent sequences: A270264 A270265 A270266 * A270268 A270269 A270270

Keyword

nonn

Author

Altug Alkan, Mar 14 2016

Extensions

More terms from Amiram Eldar, Jun 25 2019

Status

approved