A069687 Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits).

3, 5, 17, 23, 29, 47, 53, 83, 107, 113, 131, 149, 173, 197, 239, 251, 317, 359, 383, 401, 443, 503, 509, 599, 641, 683, 701, 719, 743, 797, 821, 947, 953, 1031, 1049, 1103, 1109, 1187, 1229, 1277, 1283, 1301, 1373, 1583, 1613, 1619, 1637, 1733, 1847, 1889

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

239 belongs to this sequence as 12391 is also a prime.
947 and 19471 are both primes ==> 947 is in the sequence. [From José María Grau Ribas, Jan 22 2012]

Maple

a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if isprime(parse(cat(1, p, 1))) then break fi
      od; p
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 18 2012

Mathematica

Select[ Range[2000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 1, {{1}, {-1}}]]] &]
san[i_]:=1+Prime[i]*10+10^(Floor@Log[10, Prime[i]]+2); Prime@Select[Range[1000], PrimeQ@san[#]&]  (* From José María Grau Ribas, Jan 22 2012 *)
Select[Prime[Range[300]], PrimeQ[FromDigits[Join[{1}, IntegerDigits[#], {1}]]]&]  (* Harvey P. Dale, May 18 2012 *)

Prog

(PARI) forprime( p=1, 9999, isprime(10^#Str(p*10)+p*10+1) & print1(p", ")) \\ M. F. Hasler, May 18 2012
(PARI) A069687_vec(Nmax=10^4)=my(p, d=1); vector(Nmax, i, until(isprime((d+p)*10+1), d<(p=nextprime(p+1))&d*=10); p)  \\ M. F. Hasler, May 19 2012

Crossrefs

Cf. A069688, A069689 & A069690.

Sequence in context: A152079 A027699 A153417 * A079017 A211440 A100564

Adjacent sequences: A069684 A069685 A069686 * A069688 A069689 A069690

Keyword

nonn,base

Author

Amarnath Murthy, Apr 06 2002

Extensions

Edited and extended by Robert G. Wilson v, May 03 2002

Corrected and edited following suggestions by H. P. Dale and others by M. F. Hasler, May 18 2012

Status

approved