

A175278


Base6 pandigital primes: primes having at least one of each digit 0,1,2,3,4,5 when written in base 6.


0



48761, 50033, 50051, 50069, 50101, 50207, 50231, 50311, 50461, 51131, 51137, 51151, 51461, 51503, 51511, 51721, 52181, 52391, 52541, 52571, 52583, 53731, 53881, 54091, 54121, 55001, 57191, 58481, 58901, 60161, 62591, 62921, 63029
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OFFSET

1,1


COMMENTS

Terms in this sequence have at least 7 digits in base 6, i.e., are larger than 6^6, since sum(d_i 6^i) = sum(d_i) (mod 5), and 0+1+2+3+4+5 is divisible by 5. So the smallest ones should be of the form "101...." in base 6, where "...." is a permutation of "2345". Actually there is only one such prime, cf. examples.


LINKS

Table of n, a(n) for n=1..33.


EXAMPLE

The smallest base6 pandigital prime is written "1013425" in base 6.
The next smallest such prime is "1023345"[6]; note that here the "3" is repeated, since there is no such prime of the form "102wxyz" with w=0, 1 or 2. (Using the same reasoning as in the comment, it follows that the (7digit base6 pandigital) number has the same parity as the repeated digit, which therefore must be odd to get a prime.)


PROG

(PARI) base(n, b=6)={ local(a=[n%b]); while(0<n\=b, a=concat(n%b, a)); a }
forprime(p=6^6, 6^7, #Set(base(p, 6))==6 & print1(p", "))


CROSSREFS

Sequence in context: A237146 A210401 A067869 * A336189 A157667 A176373
Adjacent sequences: A175275 A175276 A175277 * A175279 A175280 A175281


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, May 30 2010


EXTENSIONS

Edited by Charles R Greathouse IV, Aug 02 2010


STATUS

approved



