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A262366 a(n) is the n-th prime whose binary expansion begins with the binary expansion of n.

%I A262366 #13 Nov 11 2020 19:00:17
%S A262366 2,5,13,67,43,107,127,263,307,349,373,773,839,907,991,1063,1109,1201,
%T A262366 1277,1321,2713,2819,2963,3119,3229,3371,3517,3691,3779,3943,4051,
%U A262366 4217,8461,8719,8963,9241,9497,9767,10039,10303,10613,10799,11159,11317,11657,11923
%N A262366 a(n) is the n-th prime whose binary expansion begins with the binary expansion of n.
%H A262366 Alois P. Heinz, <a href="/A262366/b262366.txt">Table of n, a(n) for n = 1..5000</a>
%H A262366 <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>
%p A262366 u:= (h, t)-> select(isprime, [seq(h*2^t+k, k=0..2^t-1)]):
%p A262366 A:= proc(n, k) local l, p;
%p A262366       l:= proc() [] end; p:= proc() -1 end;
%p A262366       while nops(l(k))<n do p(k):= p(k)+1;
%p A262366         l(k):= [l(k)[], u(k,p(k))[]]
%p A262366       od: l(k)[n]
%p A262366     end:
%p A262366 a:= n-> A(n$2):
%p A262366 seq(a(n), n=1..60);
%Y A262366 Main diagonal of A262365.
%Y A262366 Cf. A077345.
%K A262366 nonn,base
%O A262366 1,1
%A A262366 _Alois P. Heinz_, Sep 20 2015