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A323176
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Prime numbers generated by the formula a(n) = round(c^((5/4)^n)), where c is the real constant given below.
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3
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113, 367, 1607, 10177, 102217, 1827697, 67201679, 6084503671, 1699344564793, 1940223714629437, 12877001925259260821, 771380135526168946568519, 722912215706743477640066820689, 21079337353575904691781436731789131951, 45166994522409258021988187061430676460306223027, 20822194129240450122637347266336444580153717439156314146339
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OFFSET
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1,1
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COMMENTS
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The constant c is given in the article [Plouffe, 2018] with 2600 digits of precision.
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LINKS
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FORMULA
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a(n) = round(c^((5/4)^n)), where c is a real constant starting 43.80468771580293481859664562569089495081037087137495184074061328752670419506...
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EXAMPLE
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a(1) = round(c^((5/4)^1)) = round(112.69...) = 113,
a(2) = round(c^((5/4)^2)) = round(367.17...) = 367,
a(3) = round(c^((5/4)^3)) = round(1607.2...) = 1607, etc..
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MAPLE
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# Computes the values according to the formula, v = 43.804..., e = 5/4, m the
# number of terms. Returns the real and the rounded values (primes).
val := proc(s, e, m)
local ll, v, n, kk;
v := s;
ll := [];
for n to m do
v := v^e; ll := [op(ll), v]
end do;
return [ll, map(round, ll)]
end;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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