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A175280 Base-9 pandigital primes: primes having at least one of each digit 0,...,8 when written in base 9. 10
393474749, 393474821, 393475373, 393481069, 393486901, 393488437, 393492797, 393494477, 393499429, 393499517, 393500741, 393528029, 393528517, 393538157, 393541693, 393544709, 393545861, 393546149, 393551189, 393551357, 393552629 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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).
MATHEMATICA
Select[Range[4*10^8], Min @ DigitCount[#, 9] > 0 && PrimeQ[#] &] (* Amiram Eldar, Apr 13 2021 *)
PROG
(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")) */
CROSSREFS
Sequence in context: A319358 A276274 A058125 * A271022 A015369 A321138
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 April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)