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A224695
Pseudoprimes to a twin prime criterion of Aebi and Cairns.
2
561, 645, 1905, 2465, 4369, 4371, 23001, 25761, 60701, 87249, 158369, 181901, 206601, 212421, 253241, 280601, 332949, 348161, 513629, 580337, 587861, 656601, 831405, 1207361, 1275681, 1472505, 1489665, 1678541, 1735841, 1815465, 1909001, 2113665, 2290641, 2419385
OFFSET
1,1
COMMENTS
Theorem 3 in the paper (see link) states that if p and p+2 are both prime then 2^(p+2) == 3*p+8 mod p(p+2). This sequence lists the pseudoprimes to this criterion.
Of the first 27 terms listed, 16 are divisible by 3.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..903 (terms below 10^11)
Christian Aebi and Grant Cairns, Catalan numbers, primes and twin primes, Elemente der Mathematik, Vol. 63, No. 4 (2008), pp. 153-164.
MAPLE
for n from 1 to 1500000 do if 2^(n+2) mod n*(n+2)=3*n+8 and not isprime(n) then print(n) fi od;
MATHEMATICA
aQ[n_] := CompositeQ[n] && PowerMod[2, n + 2, n*(n + 2)] == 3*n + 8; Select[
Range[10^6], aQ] (* Amiram Eldar, Jul 12 2019 *)
PROG
(PARI) isok(n) = (n>1) && !isprime(n) && Mod(2, n*(n+2))^(n+2) == Mod(3*n+8, n*(n+2)); \\ Michel Marcus, Jul 12 2019
CROSSREFS
Sequence in context: A074380 A215672 A085999 * A137198 A194231 A141705
KEYWORD
nonn
AUTHOR
Gary Detlefs, Apr 15 2013
EXTENSIONS
a(14) and more terms from Amiram Eldar, Jul 12 2019
STATUS
approved