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.)

3, 157, 157, 9241, 9241, 48404791, 18172964503, 50006393431, 50006393431, 181395559296673

Offset: 2

Author

Jon E. Schoenfield, Jul 16 2018

Keywords

• nonn
• base
• more

Comments

a(2)=3, the smallest term in A065720, primes whose binary representation is also the decimal representation of a prime;

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;

similarly, a(4)=157 is the smallest integer in A065720, A065721, and A065722.

Is this sequence infinite?

a(12) > 10^16. - Giovanni Resta, Aug 01 2018

Examples

			a(2)=3 because 3 is prime, 3_10 = 11_2, and 11 is prime, and 3 is the smallest such number.
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.
		

Crossrefs

Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065727.

Cf. A084482, A236537.

Extensions

a(8)-a(10) from Giovanni Resta, Jul 17 2018

a(11) from Giovanni Resta, Jul 24 2018