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A270639 Fermat pseudoprimes (A001567) that are the sum of three consecutive primes. 1

%I #17 Jun 28 2019 16:37:02

%S 13741,16705,150851,208465,249841,252601,258511,410041,486737,635401,

%T 1052503,1082401,1457773,1507963,1579249,1615681,2113921,2184571,

%U 3090091,3375487,3726541,4682833,4895065,5044033,5133201,6233977,6255341,6350941,6474691,6912079,7259161

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

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

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

%C Intersection of A001567 and A034961.

%H Amiram Eldar, <a href="/A270639/b270639.txt">Table of n, a(n) for n = 1..10000</a>

%e 4567, 4583 and 4591 are consecutive primes and their sum is 13741, a Fermat pseudoprime.

%e 84191, 84199 and 84211 are consecutive primes and their sum is 252601, a Fermat pseudoprime.

%o (PARI) isA001567(n) = {Mod(2, n)^n==2 && !ispseudoprime(n) && n > 1}

%o a034961(n) = my(p=prime(n), q=nextprime(p+1)); p+q+nextprime(q+1);

%o for(n=1, 200000, if(isA001567(a034961(n)), print1(a034961(n), ", ")));

%Y Cf. A001567, A034961, A270267.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 20 2016

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