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A175274 Base-20 pandigital primes: primes having at least one of each digit 0,...,19, when written in base 20. 4
105148064265927977839670339, 105148064265927977839838717, 105148064265927977839990337, 105148064265927977842711099, 105148064265927977843159537, 105148064265927977846038379 (list; graph; refs; listen; history; text; internal format)



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).


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.


(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))<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-20 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")) */


Cf. A138837, A050288, A175271 - A175280.

Sequence in context: A265913 A217425 A214266 * A095446 A217410 A250493

Adjacent sequences:  A175271 A175272 A175273 * A175275 A175276 A175277




M. F. Hasler, May 27 2010



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Last modified March 27 22:02 EDT 2017. Contains 284182 sequences.