This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A075173 #7 May 01 2014 02:44:55 %S A075173 0,1,2,5,8,3,128,21,34,9,32768,7,2147483648,129,10,85, %T A075173 9223372036854775808,35,170141183460469231731687303715884105728,13, %U A075173 130,32769 %N A075173 Prime factorization of n encoded by interleaving successive prime exponents in unary to bit-positions given by columns of A075300. %C A075173 As in A059884, here also we store the exponent e_i of p_i (p1=2, p2=3, p3=5, ...) in the factorization of n to the bit positions given by the column i-1 of A075300 (the exponent of 2 is thus stored to bit positions 0, 2, 4, ..., exponent of 3 to 1, 5, 9, 13, ..., exponent of 5 to 3, 11, 19, 27, 35, ...), but using unary instead of binary system, i.e. we actually store 2^(e_i) - 1 in binary. %C A075173 This injective mapping from N to N offers an example of the proof given in Cameron's book that any distributive lattice can be represented as a sublattice of the power-set lattice P(X) of some set X. This allows us to implement GCD (A003989) with bitwise AND (A004198) and LCM (A003990) with bitwise OR (A003986). Also, to test whether x divides y, it is enough to check that ((a(x) OR a(y)) XOR a(y)) = A003987(A003986(a(x),a(y)),a(y)) is zero. %D A075173 P. J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1998, page 191. (12.3. Distributive lattices) %e A075173 a(24) = 23 because 24 = 2^3 * 3^1 so we add the binary words 10101 and 10 to get 10111 in binary = 23 in decimal and a(25) = 2056 because 25 = 5^2 so we form a binary word 100000001000 = 2056 in decimal. %Y A075173 Variant: A075175. Inverse: A075174. Cf. A059884. %Y A075173 A003989(x, y) = A075174(A004198(a(x), a(y))), A003990(x, y) = A075174(A003986(a(x), a(y))). %K A075173 nonn %O A075173 1,3 %A A075173 _Antti Karttunen_, Sep 13 2002