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A306317
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Prime numbers generated by the formula a(n) = round(2^(d^n)), where d is the real constant 1.30076870414817691055252567828266106688423996320151467218595488...
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1
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2, 3, 5, 7, 13, 29, 79, 293, 1619, 14947, 269237, 11570443, 1540936027, 893681319109, 3513374197622981, 166491395148719076277, 201072926144898161374940903, 16390008340104365722976984827792343, 320076519482444467256811692239892862140322229, 7781106039755041703318535124896118983796534882794414187099
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OFFSET
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1,1
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COMMENTS
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The exponent d = 1.3007687... is the smallest found.
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LINKS
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Simon Plouffe, Table of n, a(n) for n = 1..24
Simon Plouffe, A set of formulas for primes, arXiv:1901.01849 [math.NT], 2019.
Simon Plouffe, Une formule pour les nombres premiers, viXra:1902.0036.
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FORMULA
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a(n) = round(2^(d^n)), where d is a real constant starting 1.30076870414817691055252567828266106688423996320151467218595488...
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MAPLE
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# Computes the values according to the formula, v = 2..., e = 1.30076870414817691055252567828266106688423996320151467218595488..., m the # number of terms. Returns the real and the rounded values (primes). In this case 23 terms will be generated
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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Cf. A323176, A323065, A323611.
Sequence in context: A227880 A167134 A071905 * A067573 A103199 A054217
Adjacent sequences: A306314 A306315 A306316 * A306318 A306319 A306320
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe, Feb 06 2019
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STATUS
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approved
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