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