A175280 - OEIS

%I #15 Apr 14 2021 05:24:36

%S 393474749,393474821,393475373,393481069,393486901,393488437,

%T 393492797,393494477,393499429,393499517,393500741,393528029,

%U 393528517,393538157,393541693,393544709,393545861,393546149,393551189,393551357,393552629

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

%C 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 Amiram Eldar, <a href="/A175280/b175280.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 Select[Range[4*10^8], Min @ DigitCount[#, 9] > 0 && PrimeQ[#] &] (* _Amiram Eldar_, Apr 13 2021 *)

%o (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 Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, May 30 2010

%E Edited by _Charles R Greathouse IV_, Aug 02 2010