A175278 Base-6 pandigital primes: primes having at least one of each digit 0,1,2,3,4,5 when written in base 6.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The smallest base-6 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 (7-digit base-6 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.

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