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A217428
Numbers of the form 2^r*19^s whose decimal representation contains each digit 0-9 a prime number of times.
12
611897345462967423035506688, 98653640312161724942079430255181824, 195052744758517664687371356106391552, 69210613747809022824201189555756335104, 401770033097538379880522919696423452672
OFFSET
1,1
COMMENTS
See the formula section for more data, and others in cross-reference for similar and motivation.
FORMULA
A217431(n) = 2^A217429(n) * 19^A217430(n)
EXAMPLE
2^55 * 19^8 has two copies of each of the digits 0, 1, 2, 7 and 9; three copies of each of 3, 4, 5 and 8; and five copies of the digit 6. All smaller numbers of the required type have at least a digit counted 0, 1, or a composite number of times, so this is a(1).
MATHEMATICA
nd = 50; mx = 10^nd; pr = Prime@Range@PrimePi@nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[Flatten@ Table[2^p 19^q, {p, Log[2, mx/19]}, {q, Log[19, mx/2^p]}], pQ] (* Giovanni Resta, Jan 16 2014 *)
KEYWORD
nonn,base,less
AUTHOR
James G. Merickel, Oct 05 2012
STATUS
approved