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A109718
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Periodic sequence with period {0,1,0,3}, or n^3 mod 4.
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1
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0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Since n^(2k+1) mod 4 = n^3 mod 4 for k>1 this sequence also represents n^5 mod 4; and n^7 mod 4; etc
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1).
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FORMULA
| a(n) = n^3 mod 4. G.f. = (x+3x^3)/(1-x^4).
a(n) = (1/12)*{11*(n mod 4)-7*[(n+1) mod 4]+5*[(n+2) mod 4]-[(n+3) mod 4]} - Paolo P. Lava (paoloplava(AT)gmail.com), Nov 21 2006
a(n) = (n mod 2)*(n mod 4) = (1+(-1)^(n+1))*(2+i^(n+1))/2 with i=sqrt(-1). - Bruno Berselli, Mar 14 2011
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PROG
| (Other) sage: [power_mod(n, 3, 4 )for n in xrange(0, 105)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009]
(MAGMA) &cat[[0, 1, 0, 3]: k in [0..26]]; // Bruno Berselli, Mar 14 2011
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CROSSREFS
| n mod 4 = A010873; n^2 mod 4 = A000035.
Cf. A110270; A131743. - Bruno Berselli, Mar 14 2011
Sequence in context: A155522 A007524 A204689 * A053385 A035640 A079327
Adjacent sequences: A109715 A109716 A109717 * A109719 A109720 A109721
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KEYWORD
| easy,nonn
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AUTHOR
| Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005
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