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.
%I A180933 #11 Oct 15 2024 05:13:12
%S A180933 3,13,53,222630977,3916565571106302349381
%N A180933 Initial segments of A010051, interpreted as binary numbers, that are prime.
%C A180933 The main entry for this sequence is A124077.
%C A180933 The binary expansion of all terms of this sequence is some initial segment of 1101010001010001....
%C A180933 Next terms have 642, 1268, ... decimal digits.
%C A180933 Primes in an initial portion of the infinite binary string built from the prime characteristic function A010051. - _R. J. Mathar_, Sep 26 2010
%F A180933 A000040 INTERSECT A072762. a(n) = A072762(A124077(n)). - _R. J. Mathar_, Sep 26 2010 [corrected by _Jason Yuen_, Oct 14 2024]
%e A180933 a(2) = 13, which is 1101 in binary, corresponding to the characteristic sequence of the primes: 2 is prime, 3 is prime, 4 is composite, 5 is prime.
%p A180933 A072762 := proc(n) option remember; if n =1 then return 0; elif n =2 then return 1; end if; if isprime(n) then 2*procname(n-1)+1 ; else 2*procname(n-1) ; end if; end proc:
%p A180933 for n from 1 to 300 do p := A072762(n) ; if isprime(p) then printf("%d,",p) ; end if; end do: # _R. J. Mathar_, Sep 26 2010
%o A180933 (PARI) my(n=1);for(k=3,1e4,n+=n+isprime(k);if(ispseudoprime(n),print1(n", ")))
%Y A180933 Subset of A072762.
%K A180933 nonn
%O A180933 1,1
%A A180933 _Yves Debeuret_, Sep 26 2010
%E A180933 Extended and rewritten by _Charles R Greathouse IV_, Sep 27 2010