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A316479
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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.)
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0
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OFFSET
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2,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=2..11.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065727.
Cf. A084482, A236537.
Sequence in context: A087306 A278877 A203682 * A139964 A048797 A281799
Adjacent sequences: A316476 A316477 A316478 * A316480 A316481 A316482
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KEYWORD
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nonn,base,more
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AUTHOR
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Jon E. Schoenfield, Jul 16 2018
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EXTENSIONS
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a(8)-a(10) from Giovanni Resta, Jul 17 2018
a(11) from Giovanni Resta, Jul 24 2018
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STATUS
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approved
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