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%I #32 May 11 2018 10:34:00
%S 0,0,1,8,1024,5,1071,6443,52743,1184,11131,39,7,856079,3363658,9264,
%T 3150,1313151,13,33629,555296667,534689,8388607,5,512212693,193652,
%U 286330,282030,7224372579,1120049,149041
%N Let b(n) = 2^n with n >= 2, and let c = k*b(n) + 1 for k >= 1; then a(n) is the smallest k such that c is prime and such that A007814(r(n)) = A007814(k) + n where r(n) is the remainder of 2^(b(n)/4) mod c, or 0 if no such k exists.
%C a(n-2) <= A007117(n).
%C a(33) <= 5463561471303.
%H Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Fermat factoring status</a>
%F For n >= 1, a(A204620(n)) = 3; a(A226366(n)) = 5; a(A280003(n)) = 7.
%o (PARI) print1(0, ", "0", "); for(n=4, 32, b=2^n; k=1; t=0; while(t<1, c=k*b+1; if(isprime(c), r=Mod(2, c)^(b/4); if(lift(r/b)<=k, if(valuation(lift(r), 2)==valuation(k, 2)+n, t=1; print1(k, ", ")))); k++));
%Y Cf. A007117, A007814, A298670.
%K nonn
%O 2,4
%A _Arkadiusz Wesolowski_, Jan 24 2018
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