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A063826 Let 1, 2, 3, 4 represent moves to the right, down, left and up; this sequence describes the movements in the Ulam Spiral. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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.

EXAMPLE

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.

MATHEMATICA

a[n_] := Mod[Floor[Sqrt[4*n + 1]] + 3, 4] + 1; Table[a[n], {n, 0, 104}] (* Jean-Fran├žois Alcover, Nov 30 2016 adapted from PARI *)

PROG

(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) ) } \\ Harry J. Smith, Sep 01 2009

CROSSREFS

Cf. A000267.

Sequence in context: A096827 A298321 A226142 * A152983 A205324 A213253

Adjacent sequences:  A063823 A063824 A063825 * A063827 A063828 A063829

KEYWORD

easy,nice,nonn

AUTHOR

Wai Ha Lee (Wainson(AT)hotmail.com), Aug 20 2001

STATUS

approved

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Last modified February 23 15:23 EST 2018. Contains 299581 sequences. (Running on oeis4.)