%I #5 Mar 18 2020 16:26:20

%S 3,7,29,1873,7672913,8045632442437,

%T 2490002635466567109268165355290155548689

%N Primes whose binary representation corresponds to the characteristic function of 1, 2, 3, 5, 7, ... (1 followed by primes).

%C The next term is too large to include.

%e 1873 (in base 10) = 11101010001 (in base 2).

%e ||| | | |

%e 123 5 7 11

%t Select[Table[2^(Prime[n] - 1) + Sum[2^(Prime[n] - Prime[k]), {k, 1, n}], {n, 1, 32}], PrimeQ[#] &]

%Y Primes in A333392.

%Y Cf. A000040, A004676, A008578, A080339.

%K nonn,base

%O 1,1

%A _Ilya Gutkovskiy_, Mar 18 2020