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
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Apr 14 2010
EXTENSIONS
More terms from R. J. Mathar, May 28 2010
STATUS
approved