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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

(PARI) base7(n)={ local(a=[n%7]); while(0<n\=7, a=concat(n%7, a)); a }
forprime(p=7^7, 7^7*1.1, #Set(base7(p))==7 & print1(p", "))

Crossrefs

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

Sequence in context: A115546 A233957 A224596 * A166485 A034609 A182450

Adjacent sequences: A175276 A175277 A175278 * A175280 A175281 A175282

Keyword

nonn,base

Author

M. F. Hasler, May 30 2010

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved