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Primes which are the concatenation of primes p and 2*p-1.
2

%I #15 Jan 10 2019 02:27:23

%S 23,367733,6611321,6911381,9971993,14592917,20114021,25575113,

%T 27075413,30616121,39677933,40278053,41778353,43578713,46399277,

%U 574911497,621112421,622912457,696113921,753715073,756115121,795115901,819116381,862917257,868917377,961919237,1078921577,1083721673,1131122621

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

%C All terms == 5 (mod 6).

%H Robert Israel, <a href="/A320442/b320442.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%p q:= 2*p-1;

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

%p if isprime(r) and isprime(q) then r else NULL fi;

%p end proc:

%p map(f, [2,seq(i,i=7..20000,6)]);

%o (PARI) forprime(p=1, 1e4, my(cc=eval(concat(Str(p), Str(2*p-1)))); if(ispseudoprime(2*p-1) && ispseudoprime(cc), print1(cc, ", "))) \\ _Felix Fröhlich_, Jan 09 2019

%Y Cf. A005382, A168165.

%K nonn,base

%O 1,1

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