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Search: id:A058887
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| A058887 |
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Smallest prime such that invphi((2^n)*p) is an empty set, i.e.(2^n)*p is a non-totient number. |
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4
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| 7, 17, 19, 19, 19, 31, 31, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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First 0-s in sequences were searched for k=1..256:
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FORMULA
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Min{p|p is prime and nops(invphi((2^n)*p))=0}
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EXAMPLE
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For n=1, the initial segment of {2p} sequence is nops(invphi({2p}))={4, 4, 2, 0, 2, 0, 0, 0, 2, 2, ...}, where the position of the first 0 is 4, corresponding to p(4)=7, so a(4)=4. For n=8 the same initial segment is: {11, 32, 23, 18, 24, 10, 11, 4, 9, 21, 2, 16, 9, 12, 0, 14, 5, 6, 12, ...}, where the first 0 is the 15th, corresponding to p(15)=47, thus a(15)=47. nops(invphi(47*(2^n)))=0 holds for n=1, ...1482, while inv(47*(2^1483) is not empty because 1+47*(2^1483) is a large prime q and Phi(q)=Phi(2q)=47*2^1483. Thus after n=1482, 47 has to be replaced by some other prime. For p(k), k<15 the relevant invphi sets are not empty. Do exist primes p at all, such that nops(invphi(p*2^n))=0 holds for all n or not?
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MAPLE
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[seq(nops(invphi(2^k*ithprime(i))), i=1..256)];
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CROSSREFS
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A005277, A007617, A002020, A000010, A051953.
Sequence in context: A071615 A067459 A101240 this_sequence A167797 A001913 A071845
Adjacent sequences: A058884 A058885 A058886 this_sequence A058888 A058889 A058890
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 08 2001
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