

A175278


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


8



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



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.)


MATHEMATICA

Select[Range[60000], Min @ DigitCount[#, 6] > 0 && PrimeQ[#] &] (* Amiram Eldar, Apr 13 2021 *)


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

Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175279, A175280.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



