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A187072
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Prime numbers chosen such that the even numbers that are the sum of two consecutive terms occur only once and occur as early as possible.
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3
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3, 3, 5, 5, 7, 7, 11, 5, 17, 3, 23, 5, 19, 11, 23, 13, 19, 19, 23, 17, 29, 19, 31, 13, 41, 11, 47, 13, 43, 19, 47, 17, 53, 19, 59, 17, 67, 7, 61, 19, 67, 23, 59, 29, 67, 31, 61, 41, 53, 47, 59, 53, 61, 43, 67, 41, 79, 37, 89, 29, 101, 23, 109, 13, 127, 7, 131, 5, 137, 7, 139, 11, 137, 17, 139, 13, 149, 11, 157, 7, 151, 19, 109, 67, 107, 59, 113, 67
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OFFSET
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1,1
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COMMENTS
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The even numbers a(n) + a(n+1) are in sequence A187085.
The terms for even n grow rapidly; for odd n they grow slowly. It appears that primes occur at a consistent frequency: in the first 1000000 terms, primes 3 to 23 occur about 4.7%, 4.9%, 3.4%, 2.9%, 2.6%, 2.0%, 1.8%, and 1.4% of the time. - T. D. Noe, Mar 04 2011
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LINKS
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EXAMPLE
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Primes: 3 3 5 5 7 7 11 5 17 3 23 5 19 11 23 13 19 19 23
Evens: 6 8 10 12 14 18 16 22 20 26 28 24 30 34 36 32 38 42
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MATHEMATICA
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lastE=10; eList=Range[6, lastE, 2]; evens[k_] := If[k<=Length[eList], eList[[k]], lastE+=2; AppendTo[eList, lastE]; lastE]; Join[{lastP=3}, Table[k=1; While[p=evens[k]-lastP; p<0 || !PrimeQ[p], k++]; eList=Delete[eList, k]; lastP=p, {999}]] (* T. D. Noe, Mar 04 2011 *)
s={3, 3}; ev={6}; a=3; Do[k=2; While[!FreeQ[ev, (b=a+(p=Prime[k]))], k++]; a=p; AppendTo[ev, b]; AppendTo[s, a], {3000}]; s (* Zak Seidov, Mar 03 2011 *)
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PROG
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(Haskell)
import Data.Set (Set, empty, member, insert)
a187072 n = a187072_list !! (n-1)
a187072_list = goldbach 0 a065091_list empty where
goldbach :: Integer -> [Integer] -> Set Integer -> [Integer]
goldbach q (p:ps) gbEven
| qp `member` gbEven = goldbach q ps gbEven
| otherwise = p : goldbach p a065091_list (insert qp gbEven)
where qp = q + p
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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