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A073737
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Sums of three successive terms form the odd primes.
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4
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1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 13, 9, 15, 17, 11, 19, 23, 17, 21, 29, 21, 23, 35, 25, 29, 43, 29, 31, 47, 31, 35, 61, 35, 41, 63, 45, 43, 69, 51, 47, 75, 57, 49, 85, 59, 53, 87, 71, 65, 91, 73, 69, 97, 75, 79, 103, 81, 85, 105, 87, 89, 107, 97, 103, 111, 99, 107, 125, 105, 117
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) + a(n-1) + a(n-2) = n-th prime, where a(0)=1, a(-1)=0, a(-2)=0 and the 0th prime is taken to be 1.
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EXAMPLE
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At n=10, a(10) + a(9) + a(8) = 13 + 9 + 7 = 29 = p_10.
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MATHEMATICA
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a[0] = 1; a[-1] = 0; a[-2] = 0; p[0] = 1; p[n_?Positive] := Prime[n]; a[n_] := a[n] = p[n] - a[n-1] - a[n-2]; Table[a[n], {n, 0, 69}] (* Jean-François Alcover, Sep 30 2011 *)
nxt[{a_, b_, c_}]:={b, c, NextPrime[a+b+c]-(b+c)}; Transpose[NestList[nxt, {1, 1, 1}, 70]][[1]] (* Harvey P. Dale, Mar 15 2015 *)
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PROG
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(Haskell)
a073737 n = a073737_list !! (n-1)
a073737_list =
1 : 1 : zipWith (-) a065091_list
(zipWith (+) a073737_list $ tail a073737_list)
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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STATUS
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approved
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