cp's OEIS Frontend

A316479 a(n) is the smallest prime whose base-b expansion, read as a base-10 number, is a prime for every b in 2, 3, ..., n. (For n > 10, each base-b expansion for 10 < b <= n must contain no digit larger than 9.)

%I A316479 #27 Aug 01 2018 15:46:14
%S A316479 3,157,157,9241,9241,48404791,18172964503,50006393431,50006393431,
%T A316479 181395559296673
%N A316479 a(n) is the smallest prime whose base-b expansion, read as a base-10 number, is a prime for every b in 2, 3, ..., n. (For n > 10, each base-b expansion for 10 < b <= n must contain no digit larger than 9.)
%C A316479 a(2)=3, the smallest term in A065720, primes whose binary representation is also the decimal representation of a prime;
%C A316479 a(3)=157, the smallest integer in both A065720 and A065721, primes p whose base-3 expansion is also the decimal expansion of a prime;
%C A316479 similarly, a(4)=157 is the smallest integer in A065720, A065721, and A065722.
%C A316479 Is this sequence infinite?
%C A316479 a(12) > 10^16. - _Giovanni Resta_, Aug 01 2018
%e A316479 a(2)=3 because 3 is prime, 3_10 = 11_2, and 11 is prime, and 3 is the smallest such number.
%e A316479 a(3)=157 because 157 is prime, 157_10 = 10011101_2, 157_10 = 12211_3, and 10011101 and 12211 are prime, and 157 is the smallest such number. a(4)=157 as well, since 157_10 = 2131_4 and 2131 is also prime.
%Y A316479 Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065727.
%Y A316479 Cf. A084482, A236537.
%K A316479 nonn,base,more
%O A316479 2,1
%A A316479 _Jon E. Schoenfield_, Jul 16 2018
%E A316479 a(8)-a(10) from _Giovanni Resta_, Jul 17 2018
%E A316479 a(11) from _Giovanni Resta_, Jul 24 2018