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A084662
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a(1) = 4; a(n) = a(n-1) + gcd(a(n-1), n).
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24
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4, 6, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 141, 144, 145, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
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LINKS
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MAPLE
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S := 4; f := proc(n) option remember; global S; if n=1 then S else f(n-1)+igcd(n, f(n-1)); fi; end;
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MATHEMATICA
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a[1]= 4; a[n_]:= a[n]= a[n-1] + GCD[n, a[n-1]]; Table[a[n], {n, 70}]
nxt[{n_, a_}]:= {n+1, a + GCD[a, n+1]}; NestList[nxt, {1, 4}, 70][[All, 2]] (* Harvey P. Dale, Dec 25 2018 *)
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PROG
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(Maxima) a[1]:4$ a[n]:=a[n-1]+gcd(a[n-1], n)$ makelist(a[n], n, 1, 66); /* Bruno Berselli, May 24 2011 */
(Magma) [n eq 1 select 4 else Self(n-1)+Gcd(Self(n-1), n): n in [1..66]]; // Bruno Berselli, May 24 2011
(Haskell)
a084662 n = a084662_list !! (n-1)
a084662_list =
4 : zipWith (+) a084662_list (zipWith gcd a084662_list [2..])
(SageMath)
@CachedFunction
if (n==1): return 4
else: return a(n-1) + gcd(a(n-1), n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Matthew Frank (mfrank(AT)wopr.wolfram.com) on behalf of the 2003 New Kind of Science Summer School, Jul 15 2003
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STATUS
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approved
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