A175274 Base-20 pandigital primes: primes having at least one of each digit 0,...,19, when written in base 20.

105148064265927977839670339, 105148064265927977839838717, 105148064265927977839990337, 105148064265927977842711099, 105148064265927977843159537, 105148064265927977846038379

Offset: 1

Author

M. F. Hasler, May 27 2010

Keywords

• nonn
• base

Comments

Base-20 pandigital primes must have at least 21 base-20 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

• Alonso Del Arte, Classifications of prime numbers - By representation in specific bases, OEIS Wiki as of Mar 19 2010.

Crossrefs

Cf. A138837, A050288, A175271 - A175280.

Programs

PARI

pdp( b=20/*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))