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A366287
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Numbers k such that A163511(k) is a seventh power.
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4
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0, 64, 129, 259, 519, 1039, 2079, 4159, 8192, 8319, 16385, 16512, 16639, 32771, 33025, 33152, 33279, 65543, 66051, 66305, 66432, 66559, 131087, 132103, 132611, 132865, 132992, 133119, 262175, 264207, 265223, 265731, 265985, 266112, 266239, 524351, 528415, 530447, 531463, 531971, 532225, 532352, 532479, 1048576, 1048703
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers k for which A332214(k), and also A332817(k) are seventh powers.
The sequence is defined inductively as:
(a) it contains 0 and 64,
and
(b) for any nonzero term a(n), (2*a(n)) + 1 and 128*a(n) are also included as terms.
When iterating n -> 2n+1 mod 127, starting from 64 we get 64, 2, 5, 11, 23, 47, 95, and then cycle starts again from 64 (see A153893), while on the other hand, x^7 mod 127 obtains values: 0, 1, 19, 20, 22, 24, 28, 37, 52, 59, 68, 75, 90, 99, 103, 105, 107, 108, 126. These sets have no terms in common, therefore there are no seventh powers in this sequence after the initial 0.
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LINKS
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PROG
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(PARI)
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
isA366287(n) = ispower(A163511(n), 7);
(PARI) isA366287(n) = if(n<=64, !(n%64), if(n%2, isA366287((n-1)/2), if(n%128, 0, isA366287(n>>7))));
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CROSSREFS
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Positions of multiples of 7 in A365805.
Sequence A243071(n^7), n >= 1, sorted into ascending order.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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