cp's OEIS Frontend

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.

%I A244282 #22 Feb 06 2025 13:39:46
%S A244282 23,37,53,73,113,131,137,173,179,197,311,313,317,373,379,419,431,479,
%T A244282 613,617,619,673,719,797,971,1013,1019,1031,1097,1277,1373,1499,1571,
%U A244282 1733,1811,1997,2113,2239,2293,2719,3079,3137,3313,3373,3491,3499,3593,3673,3677,3733
%N 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.
%C A244282 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.
%C A244282 Superset of A051362; a(n) first differs from A051362 when n=12.
%H A244282 Paolo P. Lava, <a href="/A244282/b244282.txt">Table of n, a(n) for n = 1..1000</a>
%e A244282 The prime number 179 is in the sequence because 17 and 79 are primes.
%p A244282 with(numtheory):
%p A244282 for m from 1 to 200 do:
%p A244282       n:=ithprime(m):x:=convert(n, base, 10):n1:=nops(x):
%p A244282       s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):
%p A244282       s2:=(n-irem(n,10))/10:
%p A244282       if type(s1,prime)=true and type(s2,prime)=true
%p A244282       then
%p A244282         printf(`%d, `, n):
%p A244282         else
%p A244282       fi:
%p A244282 od:
%t A244282 Select[Prime[Range[1000]], (id = IntegerDigits[#]; PrimeQ[FromDigits[Take[id, {1, -2}]]] && PrimeQ[FromDigits[Take[id, {2, -1}]]]) &] (* _César Eliud Lozada_, Mar 31 2024 *)
%t A244282 Select[Prime[Range[600]],With[{idp=IntegerDigits[#]},AllTrue[FromDigits/@{Rest[idp],Most[idp]},PrimeQ]]&] (* _Harvey P. Dale_, Feb 06 2025 *)
%Y A244282 Cf. A000040, A051362, A244283.
%K A244282 nonn,base
%O A244282 1,1
%A A244282 _Michel Lagneau_, Jun 25 2014
%E A244282 Inserted missing term a(49) and corrected a(50) by _Paolo P. Lava_, Dec 04 2017