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Search: id:A078972
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| A078972 |
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Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits. |
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+0
72
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| 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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"Brilliant numbers, as defined by Peter Wallrodt, are numbers with two prime factors of the same length (in decimal notation). These numbers are generally used for cryptographic purposes and for testing the performance of prime factoring programs." [Alpern]
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REFERENCES
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P. D. James, The Private Patient, Knopf, NY, 2008, p. 192. (from N. J. A. Sloane, Aug 27 2009)
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10537
Dario Alpern, Brilliant Numbers.
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EXAMPLE
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1711 = 29*59 is in the sequence since both of its factors have two digits.
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MATHEMATICA
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fQ[n_] := Block[{fi = FactorInteger@n}, Plus @@ Last /@ fi == 2 && Floor[ Log[10, fi[[1, 1]] ]] == Floor[ Log[10, fi[[ -1, 1]] ]]]; Select[ Range@792, fQ@# &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 26 2006)
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CROSSREFS
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Cf. A001358, A085647.
Sequence in context: A113433 A115654 A036326 this_sequence A115652 A084759 A054395
Adjacent sequences: A078969 A078970 A078971 this_sequence A078973 A078974 A078975
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jan 12 2003
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 27 2009
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