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A175278 Base-6 pandigital primes: primes having at least one of each digit 0,1,2,3,4,5 when written in base 6. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A237146 A210401 A067869 * A336189 A157667 A176373
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, May 30 2010
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 02 2010
STATUS
approved

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)