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A085413 Prime such that concatenation of it and its first digit is prime.

%I A085413 #12 Mar 24 2023 16:56:10
%S A085413 13,19,31,37,79,103,109,151,157,181,193,331,337,353,359,367,373,379,
%T A085413 383,751,757,787,919,941,947,953,967,971,983,1009,1021,1033,1039,1063,
%U A085413 1069,1117,1201,1249,1279,1291,1459,1483,1489,1567,1579,1597,1609,1663,1669
%N A085413 Prime such that concatenation of it and its first digit is prime.
%C A085413 Indices of primes in A085412; primes as concatenation of prime and its first digit in A085414.
%H A085413 Robert Israel, <a href="/A085413/b085413.txt">Table of n, a(n) for n = 1..10000</a>
%F A085413 Prime[A085412]
%e A085413 13 is a term because concatenation of 13 and 1 is prime.
%p A085413 R:= NULL: count:= 0:
%p A085413 for d from 1 while count < 100 do
%p A085413   for a in [1,3,7,9] do
%p A085413     for x from 1 to 10^d-1 by 2 while count < 100 do
%p A085413       if isprime(a*10^d + x) and isprime(a*10^(d+1)+10*x+a) then
%p A085413         R:= R, a*10^d+x; count:= count+1
%p A085413 fi od od od:
%p A085413 R; # _Robert Israel_, Mar 24 2023
%o A085413 (Python)
%o A085413 from itertools import count, islice
%o A085413 from sympy import isprime, primerange
%o A085413 def agen(): # generator of terms
%o A085413     for d in count(1):
%o A085413         for f in [1, 3, 7, 9]:
%o A085413             for p in primerange(f*10**d, (f+1)*10**d):
%o A085413                 if isprime(10*p+f):
%o A085413                     yield p
%o A085413 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Mar 24 2023
%Y A085413 Cf. A085412, A085414.
%K A085413 nonn,base
%O A085413 1,1
%A A085413 _Zak Seidov_, Jun 29 2003