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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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:

CROSSREFS

Cf. A000040, A051362, A244283.

Sequence in context: A268343 A063643 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

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Last modified July 20 05:37 EDT 2019. Contains 325168 sequences. (Running on oeis4.)