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

Author

M. F. Hasler, May 30 2010

Keywords

• nonn
• base

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.

Examples

			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.)
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

base(n,b=6)={ local(a=[n%b]);while(0
				

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010