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A072982
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Primes p for which the period length of 1/p is a power of 2.
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4
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3, 11, 17, 73, 101, 137, 257, 353, 449, 641, 1409, 10753, 15361, 19841, 65537, 69857, 453377, 976193, 1514497, 5767169, 5882353, 6187457, 8253953, 8257537, 70254593, 167772161, 175636481, 302078977, 458924033, 639631361, 1265011073
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OFFSET
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1,1
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COMMENTS
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All Fermat primes>5 (A019434) are in the sequence, since it can be shown that the period length of 1/(2^(2^n)+1) is 2^(2^n) whenever 2^(2^n)+1 is prime. - Benoit Cloitre, Jun 13 2007
Take all the terms from row 2^k of triangle in A046107 for k >= 0 and sort to arrive at this sequence. - Ray Chandler, Nov 04 2011
Additional terms, but not necessarily the next in sequence: 13462517317633 has period length 1048576 = 2^20; 46179488366593 has period length 2199023255552 = 2^41; 101702694862849 has period length 8388608 = 2^23; 171523813933057 has period length 4398046511104 = 2^42; 505775348776961 has period length 2199023255552 = 2^41; 834427406578561 has period length 64 = 2^6 - Ray Chandler, Nov 09 2011
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LINKS
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Ray Chandler and Robert G. Wilson v, Table of n, a(n) for n = 1..39
Index entries for sequences related to decimal expansion of 1/n
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EXAMPLE
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15361 has a period length of 256 = 2^8, hence 15361 is in the sequence.
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MATHEMATICA
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Do[ If[ IntegerQ[ Log[2, Length[ RealDigits[ 1/Prime[n]] [[1, 1]]]]], Print[ Prime[n]]], {n, 1, 47500}] (*Robert G. Wilson v*)
pmax = 10^10; p = 1; While[p < pmax, p = NextPrime[p]; If[ IntegerQ[Log[2, MultiplicativeOrder[10, p] ] ], Print[ p]; ]; ]; (*Chandler*)
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PROG
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(PARI) ? a(n)=if(n<4, n==2, znorder(Mod(10, prime(n)))) ? for(n=1, 20000, if(gcd(a(n), 2^1000)==a(n), print1(prime(n), ", ")))
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CROSSREFS
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Cf. A002371, A007138, A046107, A054471.
Cf. A197224 (power of 2 which is the period of the decimal 1/a(n)).
Sequence in context: A032008 A061368 A145701 * A124787 A080306 A036448
Adjacent sequences: A072979 A072980 A072981 * A072983 A072984 A072985
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KEYWORD
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nonn,base
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AUTHOR
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Benoit Cloitre, Jul 26 2002
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EXTENSIONS
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Edited by Robert G. Wilson v, Aug 20 2002
a(18) from Ray Chandler, May 02 2007
a(19) from Robert G. Wilson v, May 09 2007
a(20)-a(32) from Ray Chandler, May 14 2007
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STATUS
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approved
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