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Search: id:A109720
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| A109720 |
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Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7. |
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15
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| 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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this sequence also represents n^12 mod 7; n^18 mod 7; (exponents are = 0 mod 6)
Characteristic sequence for numbers n>=1 to be relatively prime to 7. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 29 2008]
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009: (Start)
a(n)=1-A082784(n); a(A047304(n))=1; a(A008589(n))=0;
A033439(n) = SUM(a(k)*(n-k): 0<=k<=n). (End)
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LINKS
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Index entries for characteristic functions [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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FORMULA
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a(n) = 0 if n=0 mod 7; a(n)= 1 else G.f. = (x+x^2+x^3+x^4+x^5+x^6)/(1-x^7)
a(n)=(1/49)*{9*(n mod 7)+2*[(n+1) mod 7]+2*[(n+2) mod 7]+2*[(n+3) mod 7]+2*[(n+4) mod 7]+2*[(n+5) mod 7]-5*[(n+6) mod 7]} - Paolo P. Lava (ppl(AT)spl.at), Nov 21 2006
Multiplicative with a(p) = (if p=7 then 0 else 1), p prime. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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PROGRAM
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(Other) sage: [power_mod(n, 6, 7)for n in xrange(0, 105)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]
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CROSSREFS
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Cf. A010876 = n mod 7; A053879 = n^2 mod 7; A070472 = m^3 mod 7; A070512 = n^4 mod 7; A070593 = n^5 mod 7.
Sequence in context: A075897 A135947 A101040 this_sequence A022932 A079421 A164980
Adjacent sequences: A109717 A109718 A109719 this_sequence A109721 A109722 A109723
Cf. A168185, A145568, A168184, A168182, A168181, A097325, A011558, A166486, A011655, A000035. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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KEYWORD
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easy,nonn,new
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AUTHOR
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Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005
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