A180933 Initial segments of A010051, interpreted as binary numbers, that are prime.

3, 13, 53, 222630977, 3916565571106302349381

Offset: 1

Author

Yves Debeuret, Sep 26 2010

Keywords

• nonn

Comments

The main entry for this sequence is A124077.

The binary expansion of all terms of this sequence is some initial segment of 1101010001010001....

Next terms have 642, 1268, ... decimal digits.

Primes in an initial portion of the infinite binary string built from the prime characteristic function A010051. - R. J. Mathar, Sep 26 2010

Examples

			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.
		

Crossrefs

Subset of A072762.

Programs

Maple

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:
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

PARI

my(n=1);for(k=3,1e4,n+=n+isprime(k);if(ispseudoprime(n),print1(n", ")))

Formula

A000040 INTERSECT A072762. a(n) = A072762(A124077(n)). - R. J. Mathar, Sep 26 2010 [corrected by Jason Yuen, Oct 14 2024]

Extensions

Extended and rewritten by Charles R Greathouse IV, Sep 27 2010