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A320445 Primes p such that 2*p-1 and the concatenation of p and 2*p-1 are primes. 1


%S 2,367,661,691,997,1459,2011,2557,2707,3061,3967,4027,4177,4357,4639,

%T 5749,6211,6229,6961,7537,7561,7951,8191,8629,8689,9619,10789,10837,

%U 11311,12619,13009,13249,13417,13681,14419,14461,14821,15121,15277,15427,15541,15667,15739,15991,16519,17137,17257

%N Primes p such that 2*p-1 and the concatenation of p and 2*p-1 are primes.

%C Primes p arising in A320442.

%C All terms but the first == 1 (mod 6).

%H Robert Israel, <a href="/A320445/b320445.txt">Table of n, a(n) for n = 1..10000</a>

%e 367 is in the sequence because 367, 2*367-1=733, and 367733 are all primes.

%p filter:= proc(p) local q, r;

%p if not isprime(p) then return false fi;

%p q:= 2*p-1;

%p r:= p*10^(1+ilog10(q))+q;

%p isprime(r) and isprime(q);

%p end proc:

%p select(filter, [2, seq(i, i=7..200000, 6)]);

%o (PARI) isok(p) = isprime(p) && isprime(2*p-1) && isprime(eval(concat(Str(p), Str(2*p-1)))); \\ _Michel Marcus_, Jan 10 2019

%Y Cf. A320442.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 09 2019

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Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)