A084482 Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

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).

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, A052027-A052033, A084482, A236356.

Sequence in context: A344862 A344861 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