This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(5)=23 because 2*5+1=11 and smallest prime of the form 11*2^m+1 is 23 (since 11+1=12 is not prime)
For n=4, 659*2^4-1 = 10543 = 13 * 811 so a(4) = 13.
[PrimeDivisors(659*2^n-1)[1]: n in [0..100]]; // Bruno Berselli, Jul 02 2014
f:= proc(m) local F;
F:= map(t -> t[1],ifactors(659*2^m-1,easy)[2]);
F:= select(type,F,integer);
if nops(F) = 0 then
F:= map(t -> t[1],ifactors(659*2^m-1)[2]);
min(F);
else min(F)
fi
end proc;
seq(f(n), n= 0 .. 100);
103 = (51+1)*2^1-1 = (25+1)*2^2-1 = (12+1)*2^3-1, the numbers 51, 25 and 12 are not primes, so 103 is in the sequence. 71 = (35+1)*2^1-1 = (17+1)*2^2-1 = (8+1)*2^3-1, the number 17 is prime, so 71 is not in the sequence.
filter := proc(n) local k;
if not isprime(n) then return false fi;
for k from 1 to padic:-ordp(n+1,2) do
if isprime((n+1)/2^k-1) then return false
fi
od:
true
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Jun 29 2016
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