A270639 Fermat pseudoprimes (A001567) that are the sum of three consecutive primes.

13741, 16705, 150851, 208465, 249841, 252601, 258511, 410041, 486737, 635401, 1052503, 1082401, 1457773, 1507963, 1579249, 1615681, 2113921, 2184571, 3090091, 3375487, 3726541, 4682833, 4895065, 5044033, 5133201, 6233977, 6255341, 6350941, 6474691, 6912079, 7259161

Offset: 1

Author

Altug Alkan, Mar 20 2016

Keywords

• nonn

Comments

In other words, Fermat pseudoprimes to base 2 of the form p + q + r where p, q and r are consecutive primes.

If a Fermat pseudoprime is the sum of n consecutive primes, it is so obvious that the minimum value of n is 3.

Intersection of A001567 and A034961.

Examples

			4567, 4583 and 4591 are consecutive primes and their sum is 13741, a Fermat pseudoprime.
84191, 84199 and 84211 are consecutive primes and their sum is 252601, a Fermat pseudoprime.
		

Links

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

Crossrefs

Cf. A001567, A034961, A270267.

Programs

PARI

isA001567(n) = {Mod(2, n)^n==2 && !ispseudoprime(n) && n > 1}
a034961(n) = my(p=prime(n), q=nextprime(p+1)); p+q+nextprime(q+1);
for(n=1, 200000, if(isA001567(a034961(n)), print1(a034961(n), ", ")));