

A175333


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


1



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
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OFFSET

1,1


COMMENTS

By a(n) "OR" prime(n), OR the respective digits, reading right to left, of a(n) and the nth 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



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:


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



