A175279 Base-7 pandigital primes: primes having at least one of each digit 0,...,6 when written in base 7.

863231, 863279, 863867, 863897, 864203, 864251, 865379, 865871, 865877, 866011, 866399, 866653, 866693, 867641, 867719, 868033, 868069, 868081, 868103, 868121, 868123, 868327, 868423, 868453, 868669, 868787, 868793, 868801, 868943, 868999

Offset: 1

Author

M. F. Hasler, May 30 2010

Keywords

• nonn
• base

Comments

Terms in this sequence have at least 8 digits in base 7, i.e., are larger than 7^7, since sum(d_i 7^i) = sum(d_i) (mod 6), and 0+1+2+3+4+5+6 is divisible by 3. So there must be at least one repeated digit, which may not be 0 nor 6 neither odd (else the resulting number is even). The smallest terms are therefore of the form "1022...." in base 7, where "...." is a permutation of "3456", cf. examples.

Examples

			The smallest base-7 pandigital primes are "10223465", "10223564", "10225364", "10225436", "10226354" and "10226453", written in base 7.
		

Links

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

Crossrefs

Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175280.

Programs

Mathematica

Select[Range[10^6], Min @ DigitCount[#, 7] > 0 && PrimeQ[#] &] (* Amiram Eldar, Apr 13 2021 *)

PARI

base7(n)={ local(a=[n%7]);while(0
				

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010