A244282 Consider a prime number p with m decimal digits. The sequence lists the primes p such that the prefix of length m-1 and the suffix of length m-1 are both prime numbers.

23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 313, 317, 373, 379, 419, 431, 479, 613, 617, 619, 673, 719, 797, 971, 1013, 1019, 1031, 1097, 1277, 1373, 1499, 1571, 1733, 1811, 1997, 2113, 2239, 2293, 2719, 3079, 3137, 3313, 3373, 3491, 3499, 3593, 3673, 3677, 3733

Offset

1,1

Comments

Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a prime p. The sequence lists the primes p such that the prefix x(0)x(1)... x(q-1) and the suffix x(1)... x(q-1)x(q) are primes.

Superset of A051362; a(n) first differs from A051362 when n=12.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

The prime number 179 is in the sequence because 17 and 79 are primes.

Maple

with(numtheory):
for m from 1 to 200 do:
      n:=ithprime(m):x:=convert(n, base, 10):n1:=nops(x):
      s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):
      s2:=(n-irem(n, 10))/10:
      if type(s1, prime)=true and type(s2, prime)=true
      then
        printf(`%d, `, n):
        else
      fi:
od:

Mathematica

Select[Prime[Range[1000]], (id = IntegerDigits[#]; PrimeQ[FromDigits[Take[id, {1, -2}]]] && PrimeQ[FromDigits[Take[id, {2, -1}]]]) &] (* César Eliud Lozada, Mar 31 2024 *)

Crossrefs

Cf. A000040, A051362, A244283.

Sequence in context: A063643 A361530 A057876 * A051362 A034302 A057878

Adjacent sequences: A244279 A244280 A244281 * A244283 A244284 A244285

Keyword

nonn,base

Author

Michel Lagneau, Jun 25 2014

Extensions

Inserted missing term a(49) and corrected a(50) by Paolo P. Lava, Dec 04 2017

Status

approved