A085413 - OEIS

%I #12 Mar 24 2023 16:56:10

%S 13,19,31,37,79,103,109,151,157,181,193,331,337,353,359,367,373,379,

%T 383,751,757,787,919,941,947,953,967,971,983,1009,1021,1033,1039,1063,

%U 1069,1117,1201,1249,1279,1291,1459,1483,1489,1567,1579,1597,1609,1663,1669

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

%C Indices of primes in A085412; primes as concatenation of prime and its first digit in A085414.

%H Robert Israel, <a href="/A085413/b085413.txt">Table of n, a(n) for n = 1..10000</a>

%F Prime[A085412]

%e 13 is a term because concatenation of 13 and 1 is prime.

%p R:= NULL: count:= 0:

%p for d from 1 while count < 100 do

%p   for a in [1,3,7,9] do

%p     for x from 1 to 10^d-1 by 2 while count < 100 do

%p       if isprime(a*10^d + x) and isprime(a*10^(d+1)+10*x+a) then

%p         R:= R, a*10^d+x; count:= count+1

%p fi od od od:

%p R; # _Robert Israel_, Mar 24 2023

%o (Python)

%o from itertools import count, islice

%o from sympy import isprime, primerange

%o def agen(): # generator of terms

%o     for d in count(1):

%o         for f in [1, 3, 7, 9]:

%o             for p in primerange(f*10**d, (f+1)*10**d):

%o                 if isprime(10*p+f):

%o                     yield p

%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, Mar 24 2023

%Y Cf. A085412, A085414.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Jun 29 2003