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Search: id:A121014
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| 1, 6, 9, 10, 15, 18, 30, 33, 45, 55, 90, 91, 99, 165, 246, 259, 370, 385, 451, 481, 495, 505, 561, 657, 703, 715, 909, 1035, 1045, 1105, 1233, 1626, 1729, 2035, 2409, 2465, 2821, 2981, 3333, 3367, 3585, 4005, 4141, 4187, 4521, 4545, 5005, 5461, 6533, 6541
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Theorem: If both numbers q and 2q-1 are primes(q is in the sequence A005382) and n=q*(2q-1) then 10^n == 10 (mod n) (n is in the sequence A121014) iff q<5 or mod(q, 20) is in the set {1, 7, 19}. 6,15,91,703,12403,38503,79003,188191,269011,... are such terms. A005939 is a subsequence of this sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 15 2006
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FORMULA
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Theorem: If both numbers q and 2q-1 are primes and n=q*(2q-1) then 10^n == 10 (mod n) (n is in the sequence) iff q<5 or mod(q, 20) is in the set {1, 7, 19}. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 11 2006
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MATHEMATICA
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Select[Range[10^4], ! PrimeQ[ # ] && PowerMod[10, #, # ] == Mod[10, # ] &] (*Chandler*)
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PROGRAM
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(PARI) for(n=1, 7000, if(!isprime(n), k=10^n; if((k-10)%n==0, print1(n, ", ")))) - (Klaus Brockhaus, Sep 06 2006)
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CROSSREFS
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Cf. A005382, A005939.
Sequence in context: A048283 A037198 A054020 this_sequence A020219 A130593 A051221
Adjacent sequences: A121011 A121012 A121013 this_sequence A121015 A121016 A121017
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Sep 06 2006
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 06 2006
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