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Primes p such that the base-10 concatenation (p+1)||p is prime.
4

%I #15 Sep 08 2022 08:46:22

%S 3,23,41,101,107,113,179,191,197,263,269,281,293,311,353,383,389,419,

%T 443,491,521,569,659,683,701,761,773,809,821,839,881,887,911,947,1109,

%U 1217,1223,1229,1433,1481,1499,1559,1667,1697,1811,1901,1973,2069,2087,2099,2111,2129

%N Primes p such that the base-10 concatenation (p+1)||p is prime.

%H Robert Israel, <a href="/A309935/b309935.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 41 is in the sequence because 41 and 4241 are primes.

%p select(t -> isprime(t) and isprime(10^(1+ilog10(t))*(t+1)+t), [$1..20000]);

%t Select[Prime[Range[350]],PrimeQ[(#+1)10^IntegerLength[#]+#]&] (* _Harvey P. Dale_, May 07 2022 *)

%o (Magma) [p:p in PrimesUpTo(2200)| IsPrime(Seqint(Intseq(p) cat Intseq(p+1)))]; // _Marius A. Burtea_, Aug 23 2019

%o (PARI) isok(k) = isprime(k) && isprime(eval(Str(k+1, k))); \\ _Jinyuan Wang_, Aug 26 2019

%K nonn,base

%O 1,1

%A _Robert Israel_, Aug 23 2019