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%I A351826 #100 Mar 31 2022 13:24:20
%S A351826 1,5,9,15,75,165,16065,137445,540645,2222535,374958045,18327149295
%N A351826 a(n) is the least k such that there are exactly n positive numbers j such that k - 2^j and k + 2^j are both prime.
%C A351826 All terms are odd. If the number j is allowed to be 0, then a(1) = 4. - _Chai Wah Wu_, Mar 24 2022
%e A351826 a(4) = 75 because 75 +/- 2^2 = 79 and 71, 75 +/- 2^3 = 83 and 67, 75 +/- 2^5 = 107 and 43, and 75 +/- 2^6 = 139 and 11 are all prime, and 75 is the least number for which there are exactly 4 such powers of 2.
%p A351826 f:= proc(n) local t,s:
%p A351826    nops(select(t -> isprime(n+2^t) and isprime(n-2^t), [$1..ilog2(n)]));
%p A351826 end proc:
%p A351826 V:= Array(0..10): count:= 0:
%p A351826 for n from 1 while count < 11 do
%p A351826   v:= f(n); if V[v] = 0 then V[v] := n; count:= count+1 fi
%p A351826 od:
%p A351826 convert(V,list);
%o A351826 (Python)
%o A351826 from itertools import count
%o A351826 from sympy import isprime
%o A351826 def A351826(n):
%o A351826     for k in count(1,2):
%o A351826         c = 0
%o A351826         for j in count(1):
%o A351826             if k-2**j < 2:
%o A351826                 break
%o A351826             if isprime(k-2**j) and isprime(k+2**j):
%o A351826                 c += 1
%o A351826             if c > n:
%o A351826                 break
%o A351826         if c == n: return k # _Chai Wah Wu_, Mar 24 2022
%K A351826 nonn,more
%O A351826 0,2
%A A351826 _J. M. Bergot_ and _Robert Israel_, Mar 24 2022
%E A351826 a(11) from _Jean-Marc Rebert_, Mar 31 2022

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