

A084482


Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.


12



50006393431, 727533146383, 2250332130313, 2651541199513, 4437592255351, 4877749016143, 6777899690983, 7417899095713, 7431376081543, 7766799025303, 9078654198463, 10712216924641, 12244626455491, 13562282568103, 14180813918071, 14833027106593, 19479075240913, 19971686697103, 23196986067193, 34431442237963, 36429184518721, 49198998504223
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OFFSET

1,1


COMMENTS

a(1) found by Jack Brennen on Jul 13 2001; remaining terms computed by Jack Brennen, Nov 15 2001.
The number must end with 1, 3, 7, or 9 in each base from 2 to 10; thus must be congruent to: 1 (mod 2), 1 (mod 3), 1 or 3 (mod 4), 1 or 3 (mod 5), 1 (mod 6), 1 or 3 (mod 7), 1 or 3 or 7 (mod 8), 1 or 7 (mod 9), 1 or 3 or 7 or 9 (mod 10).


LINKS

Table of n, a(n) for n=1..22.
Carlos Rivera, PP and P Puzzle 24: Primes in several bases


PROG

(PARI) isok(n) = sum(b=2, 10, isprime(subst(Pol(digits(n, b)), x, 10))) == 9; \\ Michel Marcus, Mar 22 2015


CROSSREFS

Cf. A052026, A038537, A052027A052033, A084482, A236356.
Sequence in context: A092381 A195283 A179228 * A216019 A303585 A034654
Adjacent sequences: A084479 A084480 A084481 * A084483 A084484 A084485


KEYWORD

nonn,base,hard,nice


AUTHOR

Jack Brennen, Jun 29 2003


EXTENSIONS

Thanks to David W. Wilson for proposing the sequence and W. Edwin Clark for verifying the terms using Maple's command isprime.


STATUS

approved



