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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
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
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
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