A249373 Prime numbers Q such that the concatenation Q,d,Q is prime for at least one d in the set {1, 2, 3, 4, 5, 6, 7, 8, 9}.

3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 193, 197, 211, 223, 229, 233, 239, 241, 257, 263, 269, 277, 281, 283, 293, 313

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

313, 353, 373 as 383 are prime numbers so a(1)=3.
727, 757, 787 as 797 are prime numbers so a(2)=7.

Mathematica

Select[Prime[Range[100]], AnyTrue[FromDigits/@Table[Join[ IntegerDigits[ #], {n}, IntegerDigits[#]], {n, 9}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 21 2016 *)

Prog

(PFGW & SCRIPT), pre10.txt file with the first 10000000 prime numbers.
SCRIPT
DIM i, 0
DIM j
DIM k
DIM n, 1
DIM o
OPENFILEOUT myf, a(n).txt
OPENFILEIN maf, pre10.txt
GETNEXT j, maf
LABEL loop1
GETNEXT j, maf
IF j>10^n THEN SET n, n+1
SET o, 0
LABEL loop2
SET o, o+1
IF o>9 THEN  GOTO loop1
SET k, j*10^(n+1)+o*10^n+j
PRP k
IF ISPRP THEN GOTO w
GOTO loop2
LABEL w
SET i, i+1
WRITE myf, j
IF i>9999 THEN END
GOTO loop1
(PARI) lista(nn) = {forprime(p=2, nn, len = #Str(p); if (sum(i=1, 9, isprime(p+(10*p+i)*10^len)), print1(p, ", ")); ); } \\ Michel Marcus, Oct 28 2014

Crossrefs

Cf. A249350, A249374, A249375, A249376, A249377, A249378, A249379, A249380, A249381.

Sequence in context: A310192 A138152 A004139 * A180346 A020632 A020596

Adjacent sequences: A249370 A249371 A249372 * A249374 A249375 A249376

Keyword

nonn,base

Author

Pierre CAMI, Oct 27 2014

Status

approved