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Search: id:A065882
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| A065882 |
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Ultimate modulo 4: right-hand nonzero digit of n when written in base 4. |
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+0
5
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| 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
Index entries for sequences related to final digits of numbers
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FORMULA
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If n mod 4 = 0 then a(n) = a(n/4), otherwise a(n) = n mod 4. a(n) = A065883(n) mod 4.
Fixed point of the morphism : 1 ->1231, 2 ->1232, 3 ->1233, starting from a(1) = 1 . Sequence read mod 2 gives A035263. a(n) = A007913(n) mod 4. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 28 2004
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EXAMPLE
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a(7)=3 and a(112)=3, since 7 is written in base 4 as 13 and 112 as 1300.
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MATHEMATICA
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Nest[ Flatten[ # /. {1 -> {1, 2, 3, 1}, 2 -> {1, 2, 3, 2}, 3 -> {1, 2, 3, 3}}] &, {1}, 4] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2005)
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PROGRAM
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(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x%b; x\=b; e+=d*f; f*=10); return(e) } { for (n=1, 1000, a=baseE(n, 4); while (a%10 == 0, a\=10); write("b065882.txt", n, " ", a%10) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 03 2009]
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CROSSREFS
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In base 2 this is A000012, base 3 A060236 and base 10 A065881. Cf. A010873, A065883.
Sequence in context: A070913 A114280 A123564 this_sequence A007884 A157813 A111879
Adjacent sequences: A065879 A065880 A065881 this_sequence A065883 A065884 A065885
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KEYWORD
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base,nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Nov 26 2001
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