Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Oct 15 2024 05:13:12
%S 3,13,53,222630977,3916565571106302349381
%N Initial segments of A010051, interpreted as binary numbers, that are prime.
%C The main entry for this sequence is A124077.
%C The binary expansion of all terms of this sequence is some initial segment of 1101010001010001....
%C Next terms have 642, 1268, ... decimal digits.
%C Primes in an initial portion of the infinite binary string built from the prime characteristic function A010051. - _R. J. Mathar_, Sep 26 2010
%F A000040 INTERSECT A072762. a(n) = A072762(A124077(n)). - _R. J. Mathar_, Sep 26 2010 [corrected by _Jason Yuen_, Oct 14 2024]
%e 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 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 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 (PARI) my(n=1);for(k=3,1e4,n+=n+isprime(k);if(ispseudoprime(n),print1(n", ")))
%Y Subset of A072762.
%K nonn
%O 1,1
%A _Yves Debeuret_, Sep 26 2010
%E Extended and rewritten by _Charles R Greathouse IV_, Sep 27 2010