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A175280 Base-9 pandigital primes: primes having at least one of each digit 0,...,8 when written in base 9.

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%I A175280 #15 Apr 14 2021 05:24:36
%S A175280 393474749,393474821,393475373,393481069,393486901,393488437,
%T A175280 393492797,393494477,393499429,393499517,393500741,393528029,
%U A175280 393528517,393538157,393541693,393544709,393545861,393546149,393551189,393551357,393552629
%N A175280 Base-9 pandigital primes: primes having at least one of each digit 0,...,8 when written in base 9.
%C A175280 Terms in this sequence have at least 10 digits in base 9, i.e., are larger than 9^9, since sum(d_i 9^i) = sum(d_i) (mod 8), and 0+1+2+3+4+5+6+7+8 is divisible by 4. So there must be at least one repeated digit, which may not be even, else the resulting number is even. The smallest terms are therefore of the form "10123...." in base 9, where "...." is a permutation of "45678", cf. examples.
%H A175280 Amiram Eldar, <a href="/A175280/b175280.txt">Table of n, a(n) for n = 1..10000</a>
%e A175280 The first terms of this sequence, i.e., smallest base-9 pandigital primes, are "1012346785", "1012346875", "1012347658", "1012356487", "1012365487", "1012367584", "1012374568", "1012376845", "1012384657", ... (written in base 9).
%t A175280 Select[Range[4*10^8], Min @ DigitCount[#, 9] > 0 && PrimeQ[#] &] (* _Amiram Eldar_, Apr 13 2021 *)
%o A175280 (PARI) pdp( b=9/*base*/, c=99/* # of terms to produce */) = { my(t, a=[], bp=vector(b,i,b^(b-i))~, offset=b*(b^b-1)/(b-1)); for( i=1,b-1, offset+=b^b; for( j=0,b!-1, isprime(t=offset-numtoperm(b,j)*bp) | next; #(a=concat(a,t))<c | return(vecsort(a))))} /* NOTE: Due to the implementation of numtoperm, the returned list may be incomplete towards its end. Thus computation of more than the required # of terms is recommended. [The initial digits of the base-9 expansion of the terms allow one to know up to where it is complete.] One may use a construct of the form: vecextract(pdp(9,199),"1..20")) */
%Y A175280 Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279.
%K A175280 nonn,base
%O A175280 1,1
%A A175280 _M. F. Hasler_, May 30 2010
%E A175280 Edited by _Charles R Greathouse IV_, Aug 02 2010