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A175273
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Base-16 pandigital primes.
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8
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18528729602926047181, 18528729602926100221, 18528729602926108411, 18528729602926112701, 18528729602926116331, 18528729602926234591, 18528729602926235071, 18528729602927029471, 18528729602927225551
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OFFSET
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1,1
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COMMENTS
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Base-16 (a.k.a. hexadecimal, sexadecimal, senidenary or hexadecadic) pandigital primes must have at least 17 hexadecimal digits (i.e. they are larger than 16^16 = 2^64 > 10^19), since sum(d_i 16^i) = sum(d_i) (mod 15), and 0+1+...+14+15 is divisible by 15. So the smallest ones should be of the form "101234567...." in base 16, where "...." is a permutation of "89ABCDEF".
The same reasoning shows that numbers of this form ("1012...") are congruent to 1 modulo 15 and thus modulo 30 (since also = 1 [mod 2]). This explains that all terms < 2*16^16 end in the (decimal!) digit 1.
a(n) == 1 (mod 30) for a(n) < 2^65 = 3.69*10^19.
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LINKS
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PROG
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(PARI) pdp( b=16/*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-16 expansion of the terms allow one to know up to where it is complete.] You may use a construct of the form: vecextract(pdp(16, 999), "1..20")) */
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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