

A175274


Base20 pandigital primes: primes having at least one of each digit 0,...,19, when written in base 20.


4



105148064265927977839670339, 105148064265927977839838717, 105148064265927977839990337, 105148064265927977842711099, 105148064265927977843159537, 105148064265927977846038379
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OFFSET

1,1


COMMENTS

Base20 pandigital primes must have at least 21 base20 digits (i.e. they are larger than 20^20 > 10^26), since sum(d_i 20^i) = sum(d_i) (mod 19), and 0+1+...+18+19 is divisible by 19. So the smallest ones should be of the form "10123456789ABCD..." in base 20, where "..." is a permutation of "EFHGIJ" (with A..J representing digits 10..19).


LINKS

Table of n, a(n) for n=1..6.
Alonso Del Arte, Classifications of prime numbers  By representation in specific bases, OEIS Wiki as of Mar 19 2010.


PROG

(PARI) pdp( b=20/*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 base20 expansion of the terms allow one to know up to where it is complete.] You may use a construct of the form: vecextract(pdp(20, 999), "1..20")) */


CROSSREFS

Cf. A138837, A050288, A175271  A175280.
Sequence in context: A265913 A217425 A214266 * A095446 A217410 A250493
Adjacent sequences: A175271 A175272 A175273 * A175275 A175276 A175277


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, May 27 2010


STATUS

approved



