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Primes obtained from other primes by prefixing a 6.
3

%I #18 May 12 2024 11:28:55

%S 67,613,617,619,631,641,643,647,653,659,661,673,683,6101,6113,6131,

%T 6151,6163,6173,6197,6199,6211,6229,6257,6263,6269,6271,6277,6311,

%U 6317,6337,6353,6359,6367,6373,6379,6389,6397,6421,6449,6491,6521,6547,6563

%N Primes obtained from other primes by prefixing a 6.

%H Robert Israel, <a href="/A289867/b289867.txt">Table of n, a(n) for n = 1..10000</a>

%e 613 is a term because it is a prime obtained by prefixing a 6 to the prime 13.

%e 6101 is a term because it is a prime obtained by prefixing a 6 to the prime 101.

%p p:= 0: A:= NULL:

%p while p < 1000 do

%p p:= nextprime(p);

%p q:= 10^(ilog10(p)+1)*6+p;

%p if isprime(q) then A:= A, q; fi

%p od:

%p A; # _Robert Israel_, Jul 17 2017

%t Select[Table[FromDigits[Join[IntegerDigits[6], IntegerDigits[Prime[n]]]], {n, 110}], PrimeQ]

%t Select[6*10^IntegerLength[#]+#&/@Prime[Range[150]],PrimeQ] (* _Harvey P. Dale_, Apr 03 2022 *)

%o (Magma) [k: p in PrimesUpTo(800) | IsPrime(k) where k is Seqint(Intseq(p) cat [6])];

%o (PARI) terms(n) = my(i=0); forprime(p=1, , my(s=eval(Str(6, p))); if(ispseudoprime(s), print1(s, ", "); i++); if(i==n, break))

%o /* Print initial 50 terms as follows */

%o terms(50) \\ _Felix Fröhlich_, Jul 15 2017

%Y Cf. similar sequences listed in A289866.

%K nonn,base

%O 1,1

%A _Vincenzo Librandi_, Jul 15 2017