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%I #16 May 14 2024 02:25:10
%S 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,
%T 29,23,19,31,2,127,127,127,107,107,103,127,89,83,79,79,67,127,59,59,
%U 47,37,29,31,23,17,31,5,8191,251,251,241,239,239,229,223,223,223,199,199
%N a(n) is the smallest prime such that (binary a(n)) OR (binary prime(n)) is one less than a power of 2.
%C 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.
%C Each digit of binary a(n) OR'ed with the respective (reading right to left) digit of binary prime(n) is 1.
%H John Tyler Rascoe, <a href="/A175333/b175333.txt">Table of n, a(n) for n = 1..1028</a>
%e 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.
%p read("transforms");
%p 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:
%p seq(A175333(n),n=1..80) ; # _R. J. Mathar_, May 28 2010
%Y Cf. A007053.
%K base,nonn
%O 1,1
%A _Leroy Quet_, Apr 14 2010
%E More terms from _R. J. Mathar_, May 28 2010
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