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A175280
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Base-9 pandigital primes: primes having at least one of each digit 0,...,8 when written in base 9.
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10
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393474749, 393474821, 393475373, 393481069, 393486901, 393488437, 393492797, 393494477, 393499429, 393499517, 393500741, 393528029, 393528517, 393538157, 393541693, 393544709, 393545861, 393546149, 393551189, 393551357, 393552629
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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Select[Range[4*10^8], Min @ DigitCount[#, 9] > 0 && PrimeQ[#] &] (* Amiram Eldar, Apr 13 2021 *)
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PROG
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(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")) */
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CROSSREFS
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Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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