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A177904
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a(1)=a(2)=a(3)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor".
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10
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1, 1, 1, 3, 5, 3, 11, 19, 11, 41, 71, 41, 17, 43, 101, 23, 167, 97, 41, 61, 199, 43, 101, 7, 151, 37, 13, 67, 13, 31, 37, 3, 71, 37, 37, 29, 103, 13, 29, 29, 71, 43, 13, 127, 61, 67, 17, 29, 113, 53, 13, 179, 7, 199, 11, 31, 241, 283, 37, 17, 337, 23, 29, 389, 7, 17, 59, 83, 53, 13, 149, 43, 41, 233, 317, 197, 83, 199, 479, 761, 1439, 47, 107
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OFFSET
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1,4
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COMMENTS
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After 86 steps, enters a cycle of length 212 (see A177923).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..1000
G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362.
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MAPLE
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with(numtheory, divisors); A006530 := proc(n) local i, t1, t2, t3, t4, t5; t1 := divisors(n); t2 := convert(t1, list); t3 := sort(t2); t4 := nops(t3); t5 := 1; for i from 1 to t4 do if isprime(t3[t4+1-i]) then RETURN(t3[t4+1-i]); fi; od; 1; end;
M:=1000;
t1:=[1, 1, 1];
for n from 4 to M do
t1:=[op(t1), A006530(t1[n-1]+t1[n-2]+t1[n-3])]; od:
t1;
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MATHEMATICA
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nxt[{a_, b_, c_}]:={b, c, FactorInteger[a+b+c][[-1, 1]]}; NestList[nxt, {1, 1, 1}, 90][[All, 1]] (* Harvey P. Dale, Jul 17 2017 *)
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PROG
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(Haskell)
a177904 n = a177904_list !! (n-1)
a177904_list = 1 : 1 : 1 : (map a006530 $ zipWith (+)
a177904_list (tail $ zipWith (+) a177904_list $ tail a177904_list))
-- Reinhard Zumkeller, Jul 24 2012
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CROSSREFS
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Cf. A006530, A175723, A178174, A178095, A214320.
Sequence in context: A345014 A328878 A178095 * A049072 A059887 A023585
Adjacent sequences: A177901 A177902 A177903 * A177905 A177906 A177907
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 16 2010
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STATUS
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approved
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