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A132129 Largest prime with distinct digits when written in base n. 0
2, 19, 19, 577, 7417, 114229, 2053313, 42373937, 987654103 (list; graph; refs; listen; history; internal format)
OFFSET

2,1

COMMENTS

a(10) = 987654103 = A007810(9). For n >= 3, a(n) < A062813(n), a multiple of n.

Contribution R. J. Mathar, May 15 2010 (START):

Supposed all digits are used and the digits at positions 0 to n-1 are d_0, d_1,... d_{n-1}, the candidates are d_0+d_1*n+d_2*n^2+....+d_{n-1}*n^(n-1).

These values are (n-1)*n/2 (mod n-1), and they cannot be prime if n is even, because this number is = 0 (mod n-1) then, showing that n-1 is a divisor.

In conclusion, if n is even, the entries have at most n-1 digits in base n , which

yields a(11) >= 25678048763, a(12) = 736867805209, a(13) >= 23136292864193,

a(14) = 789018236128391, a(15) >= 29043982525257901, a(16) = 1147797409030815779. (END)

EXAMPLE

a(9) = 42373937 as the prime 42373937 (base 10) = 87654102 (base 9), the largest prime number with distinct digits when represented in base 9.

CROSSREFS

Cf. A062813, A007810, A029743.

Sequence in context: A153653 A065643 A038031 * A125611 A022119 A042247

Adjacent sequences:  A132126 A132127 A132128 * A132130 A132131 A132132

KEYWORD

base,nonn

AUTHOR

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 11 2007

EXTENSIONS

Removed my claim of finiteness of the sequence. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2010

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Last modified February 17 16:49 EST 2012. Contains 206058 sequences.