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A309749 Primes p such that the base-10 concatenations (p+1)||p and (p+1)||(p+1)||p are both prime. 1
3, 197, 263, 281, 443, 881, 887, 947, 2111, 2129, 2237, 2699, 2741, 2897, 3251, 3539, 3821, 3881, 4049, 4451, 4523, 4787, 6257, 6389, 8609, 8741, 10163, 10193, 10247, 11027, 13187, 14591, 14897, 16193, 16901, 17027, 18797, 19319, 19379, 20147, 20681, 21563, 21647, 22073, 22259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) == 5 (mod 6) for n >= 2.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 263 is in the sequence because 263, 264263 and 264264263 are all prime.

MAPLE

filter:= proc(n) local v, w, q;

  if not isprime(n) then return false fi;

  v:= 10^(1+ilog10(n));

  q:= v*(n+1)+n;

  if not isprime(q) then return false fi;

  isprime((10^(1+ilog10(q))+v)*(n+1)+n)

end proc:

select(filter, [3, seq(i, i=5..100000, 6)]);

MATHEMATICA

pcQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n+1]}, AllTrue[ {FromDigits[ Join[ idn2, idn]], FromDigits[ Join[idn2, idn2, idn]]}, PrimeQ]]; Select[Prime[Range[2500]], pcQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 11 2019 *)

PROG

(MAGMA) [p:p in PrimesUpTo(23000)|IsPrime(Seqint(Intseq(p) cat Intseq(p+1))) and IsPrime(Seqint(Intseq(p) cat Intseq(p+1) cat Intseq(p+1)))]; // Marius A. Burtea, Aug 27 2019

CROSSREFS

Cf. A309935.

Sequence in context: A093978 A101382 A000724 * A209120 A256407 A256406

Adjacent sequences:  A309746 A309747 A309748 * A309750 A309751 A309752

KEYWORD

nonn,base

AUTHOR

Robert Israel, Aug 26 2019

STATUS

approved

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)