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Search: id:A063670
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| A063670 |
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Positions of nonzero coefficients in cyclotomic polynomial Phi_n(x), converted from binary to decimal. |
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+0
3
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| 2, 3, 3, 7, 5, 31, 7, 127, 17, 73, 31, 2047, 21, 8191, 127, 443, 257, 131071, 73, 524287, 341, 7003, 2047, 8388607, 273, 1082401, 8191, 262657, 5461, 536870911, 443, 2147483647, 65537, 1797851, 131071, 26181091, 4161, 137438953471, 524287
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OFFSET
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0,1
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COMMENT
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a(n)=2^n-1 whenever n is prime. It seems as if a(n) >= A005420(n) for all n (checked up to 200), with equality for all 1<n<20 except {11,12,15} and whenever A005420(n)=2^n-1 (i.e., 2^n-1 is prime). - M. F. Hasler (maximilian.hasler(AT)gmail.com), Apr 30 2007
a(0) could also be 1. - T. D. Noe, Oct 29 2007
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 0..1000
Index entries for cyclotomic polynomials, positions of coefficients
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MAPLE
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[seq(Phi_pos_terms(j, 2)+Phi_neg_terms(j, 2), j=0..104)];
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PROGRAM
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(PARI) A063670(n)=local(p=polcyclo(n+!n)); if(n, sum(i=0, n, (polcoeff(p, i)<>0)<<i), 2) - M. F. Hasler (maximilian.hasler(AT)gmail.com), Apr 30 2007
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CROSSREFS
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A013594, A063670[n] = A063696[n] (the positive terms) + A063698[n] (the negative terms). This sequence in binary: A063671.
Cf. A005420.
Sequence in context: A141061 A076557 A140407 this_sequence A171824 A143444 A108346
Adjacent sequences: A063667 A063668 A063669 this_sequence A063671 A063672 A063673
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Aug 03 2001
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