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A116981
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Number of distinct representations of 8n^3 as the sum of two primes.
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0
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1, 5, 13, 11, 28, 53, 50, 53, 135, 106, 116, 253, 165, 229, 568, 244, 313, 656, 381, 575, 1123, 600, 612, 1297, 956, 871, 1735, 1130, 1102, 3025, 1288, 1314, 3169, 1620, 2671, 3582, 1954, 2149, 4729, 3064
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| H. Halberstam and H. E. Richert, "Sieve methods", Academic Press, London, New York, San Francisco, 1974.
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FORMULA
| a(n) = #{p(i) + p(j) = (2n)^3 for p(k) = A000040(k) and i >= j}. a(n) = #{p(i) + p(j) = A016743(n) for p(k) = A000040(k) and i >= j}.
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EXAMPLE
| a(1) = 1 because (2*1)^3 = 8 = 3 + 5 uniquely.
a(2) = 5 because (2*2)^3 = 64 = 3 + 61 = 5 + 59 = 11 + 53 = 17 + 47 = 23 + 41.
a(3) = 13 because (2*3)^3 = 216 = 5 + 211 = 17 + 199 = 19 + 197 = 23 + 193 = 37 + 179 = 43 + 173 = 53 + 163 = 59 + 157 = 67 + 149 = 79 + 137 = 89 + 127 = 103 + 113 = 107 + 109.
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MAPLE
| a:=proc(n) local ct, j: ct:=0: for j from 1 to prevprime((2*n)^3) do if isprime((2*n)^3-ithprime(j))=true then ct:=ct+1 else ct:=ct fi od: ct/2: end: seq(a(n), n=1..40); # execution takes hours - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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CROSSREFS
| Cf. A000040, A016742, A016743.
Sequence in context: A175484 A156682 A089534 * A094150 A130502 A051899
Adjacent sequences: A116978 A116979 A116980 * A116982 A116983 A116984
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 01 2006
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EXTENSIONS
| Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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