

A175279


Base7 pandigital primes: primes having at least one of each digit 0,...,6 when written in base 7.


9



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
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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 base7 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



