A175333 a(n) is the smallest prime such that (binary a(n)) OR (binary prime(n)) is one less than a power of 2.

3, 2, 2, 2, 5, 2, 31, 13, 11, 2, 2, 31, 23, 23, 17, 11, 5, 2, 61, 59, 127, 53, 47, 47, 31, 31, 29, 23, 19, 31, 2, 127, 127, 127, 107, 107, 103, 127, 89, 83, 79, 79, 67, 127, 59, 59, 47, 37, 29, 31, 23, 17, 31, 5, 8191, 251, 251, 241, 239, 239, 229, 223, 223, 223, 199, 199

Offset

1,1

Comments

By a(n) "OR" prime(n), OR the respective digits, reading right to left, of a(n) and the n-th prime written in binary.

Each digit of binary a(n) OR'ed with the respective (reading right to left) digit of binary prime(n) is 1.

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..1028

Example

19, the 8th prime, in binary is 10011. The smallest number that when written in binary and OR'ed with 10011, then it is a power of 2 minus 1, is 12 (1100 in binary). But 12 is not a prime. The next larger number that works, which is a prime, is 13 (1101 in binary). OR'ing the respective digits of 10011 and 01101 (with appropriate leading 0), from right to left, is: 1 OR 1 = 1; 1 OR 0 = 1; 0 OR 1 = 1; 0 OR 1 = 1; and 1 OR 0 = 1. Since all pairs of respective digits OR'ed equal 1 (and the resulting binary number represents a power of 2 minus 1), then a(8) = 13.

Maple

read("transforms");
A175333 := proc(n) local i, p, a ; for i from 1 do p := ithprime(i) ; a := ORnos(p, ithprime(n)) +1 ; if numtheory[factorset](a) = {2} then return p; end if; end do: end proc:
seq(A175333(n), n=1..80) ; # R. J. Mathar, May 28 2010

Crossrefs

Cf. A007053.

Sequence in context: A024703 A102845 A064126 * A130845 A134653 A377320

Adjacent sequences: A175330 A175331 A175332 * A175334 A175335 A175336

Keyword

base,nonn

Author

Leroy Quet, Apr 14 2010

Extensions

More terms from R. J. Mathar, May 28 2010

Status

approved