

A175280


Base9 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

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

The first terms of this sequence, i.e., smallest base9 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^(bi))~, offset=b*(b^b1)/(b1)); for( i=1, b1, offset+=b^b; for( j=0, b!1, isprime(t=offsetnumtoperm(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 base9 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

Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279.
Sequence in context: A319358 A276274 A058125 * A271022 A015369 A321138
Adjacent sequences: A175277 A175278 A175279 * A175281 A175282 A175283


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, May 30 2010


EXTENSIONS

Edited by Charles R Greathouse IV, Aug 02 2010


STATUS

approved



