A331205
a(n) = least prime of the form 2^m - 2^n + 1.
Original entry on oeis.org
2, 3, 5, 549755813881, 17, 97, 193, 140737488355201, 257, 7681, 15361, 134215681, 12289, 8380417, 114689
Offset: 0
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for(n=0,14, for(m=n+1,oo, k=2^m-2^n+1; if(isprime(k), print1(k,", "); break)))
A331217
a(n) is the least prime of the form 2^m - 2^n - 1.
Original entry on oeis.org
2, 5, 3, 7, 47, 31, 191, 127, 16127, 3583, 15359, 6143, 1044479, 8191, 245759, 16744447, 4128767, 131071, 786431, 524287, 274876858367, 14680063, 4398042316799, 260046847, 4278190079, 4261412863, 1125899839733759, 576460752169205759, 16911433727
Offset: 0
a(1) = 2: 2^2 - 2^0 - 1 = 2, thus exponent 2 = A181692(0);
a(2) = 5: 2^3 - 2^1 - 1 = 5, 2^2 - 2^1 - 1 = 1 is not a prime, A181692(1) = 3;
a(4) = 47: 2^6 - 2^4 - 1 = 31, whereas the first candidate 2^5 - 2^4 - 1 = 15 is composite.
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a:=[]; for n in [0..30] do m:=n+1; while not IsPrime(2^m-2^n-1) do m:=m+1; end while; Append(~a,2^m-2^n-1); end for; a; // Marius A. Burtea, Jan 13 2020
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f:= proc(n) local m, p;
p:= -1;
for m from n do
p:= p + 2^m;
if isprime(p) then return p fi
od
end proc:
map(f, [$0..30]); # Robert Israel, Jan 13 2020
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a[n_] := For[m = n+1, True, m++, If[PrimeQ[p = 2^m-2^n-1], Return[p]]];
a /@ Range[0, 28] (* Jean-François Alcover, Oct 25 2020 *)
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for(n=0,28, for(m=n+1,oo, k=2^m-2^n-1; if(isprime(k), print1(k,", "); break)))
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