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A063826
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Let 1, 2, 3, 4 represent moves to the right, down, left and up; this sequence describes the movements in the Ulam Spiral.
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17
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1, 2, 3, 3, 4, 4, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
D. Alpern, Ulam's Spiral
Adrian J. F. Leatherland (bunyip(AT)yoyo.cc.monash.edu.au), The mysterious Ulam spiral phenomenon
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FORMULA
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Sequence starts with 1, 2, 3, then can be broken into groups of 8n+4 members, so if n is incremented, starting at 1, the groups follow the following pattern: 3 occurs at the beginning of the group, 4 then occurs 2n times, 1 occurs 2n+1 times, 2 occurs 2n+1 times, 3 occurs 2n+1 times; so each group has 8n+4 terms.
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EXAMPLE
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Breaking into the groups, we have: 1, 2, 3 n=1: 3, 4, 4, 1, 1, 1, 2, 2, 2, 3, 3, 3, n=2: 3, 4, 4, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3 n=3: 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3 and so on.
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PROG
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(PARI) a(n)=if(n<0, 0, (sqrtint(4*n+1)+3)%4+1)
(PARI) { for (n=0, 1000, write("b063826.txt", n, " ", (sqrtint(4*n + 1) + 3)%4 + 1) ) } [From Harry J. Smith, Sep 01 2009]
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CROSSREFS
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Cf. A000267.
Sequence in context: A038203 A186971 A096827 * A152983 A205324 A213253
Adjacent sequences: A063823 A063824 A063825 * A063827 A063828 A063829
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Wai Ha Lee (Wainson(AT)hotmail.com), Aug 20 2001
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STATUS
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approved
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