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

1,1

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.

Links

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

Example

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.

Prog

(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), ", ")));

Crossrefs

Cf. A001567, A034961, A270267.

Sequence in context: A370504 A370503 A235184 * A031807 A119730 A204839

Adjacent sequences: A270636 A270637 A270638 * A270640 A270641 A270642

Keyword

nonn

Author

Altug Alkan, Mar 20 2016

Status

approved