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Search: id:A053148
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| A053148 |
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When cototient function (A051953) is iterated with initial value A002110(n), a(n) = exponent of the largest power of 2 which appears in the iteration. |
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1
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| 1, 2, 3, 5, 5, 8, 5, 9, 8, 16, 6, 9, 12, 8, 9, 7, 4, 11, 6, 6, 9, 13, 8, 13, 11, 17, 7, 13, 20, 4, 11, 11, 15, 13, 9, 19
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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1. In these iteration chains the number of non-2-powers seem to be dominant. 2. The sequence is not monotonic.
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EXAMPLE
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n=10, the iteration chain of 43 terms is {6469693230,5447823150,4315810350,...,188416,98304,65536,32768,...,4,2,1,0} in which 65536 is the largest power of 2 is 2^14, a(10)=16 for n=11 the length is 61, including 54 non-2 powers,7 powers of 2,of which the largest is 2^6 thus a(11)=6 while a(10)=16.
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PROGRAM
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(PARI) A051953(n)= { return(n-eulerphi(n)); } A002110(n)= { return(prod(i=1, n, prime(i))); } ispow2(n)= { local(nbin, nbinl, sd); nbin=binary(n); nbinl=matsize(nbin); sd=sum(i=1, nbinl[2], nbin[i]); if(sd==1, return(nbinl[2]-1), return(0); ); } A053148itr(n)= { local(v, vbin, maxp); v=A002110(n); maxp=ispow2(v); while(v>0, v=A051953(v); maxp=max(maxp, ispow2(v)); ); return(maxp); } { for(n=1, 70, print1(A053148itr(n), ", "); ); } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2006
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CROSSREFS
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A002110, A051953.
Sequence in context: A121380 A019759 A019965 this_sequence A072728 A095413 A134871
Adjacent sequences: A053145 A053146 A053147 this_sequence A053149 A053150 A053151
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 28 2000
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2006
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