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A005518
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Largest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling.
(Formerly M1154)
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14
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1, 2, 4, 8, 19, 67, 331, 2221, 19577, 219613, 3042161, 50728129, 997525853, 22742734291, 592821132889, 17461204521323, 575411103069067, 21034688742654437, 846729487306354343
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OFFSET
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1,2
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COMMENTS
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Let prime(1)=2, ... denote the primes. The label f(T) for a rooted tree T is 1 if T has 1 node, otherwise f(T) = Product prime(f(T_i)) where the T_i are the subtrees obtained by deleting the root and the edges adjacent to it.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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I. Gutman and A. Ivić, On Matula numbers, Discrete Math., Vol. 150, No. 1-3 (1996), pp. 131-142.
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FORMULA
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a(1)=1; a(2)=2; a(3)=4; a(4)=8; a(n) = the a(n-1)-th prime (see the Gutman and Ivic 1994 paper). - Emeric Deutsch, Apr 15 2012
Under plausible assumptions about the growth of the primes, for n >= 4, a(n+1) = a(n)-th prime and A005518(n) = A057452(n-3). - David W. Wilson, Jul 09 2001
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MAPLE
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with(numtheory): a := proc (n) if n = 1 then 1 elif n = 2 then 2 elif n = 3 then 4 elif n = 4 then 8 else ithprime(a(n-1)) end if end proc: seq(a(n), n = 1 .. 12); # Emeric Deutsch, Apr 15 2012
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MATHEMATICA
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a[n_] := a[n] = Switch[n, 1, 1, 2, 2, 3, 4, 4, 8, _, Prime[a[n-1]]]; Table[a[n], {n, 1, 16}] (* Jean-François Alcover, Mar 06 2014, after Emeric Deutsch *)
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CROSSREFS
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Apart from initial terms, same as A057452.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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