OFFSET
1,2
COMMENTS
Restricted growth sequence transform of triple [A319990(n), A319991(n), A319992(n)], or equally, of ordered pair [A320010(n), A320013(n)].
Apart from trivial cases of primes, all other duplicates in range 1 .. 65537 seem to be squarefree semiprimes of the form 3k+1, i.e., both prime factors are either of the form 3k+1 or of the form 3k+2. Question: Is there any reason that more complicated cases would not occur later?
Differs from A319693 first for n = 108. - Georg Fischer, Oct 16 2018
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
The first set of numbers that forms a nontrivial equivalence class is [295, 583, 799, 943] = [5*59, 11*53, 17*47, 23*41]. The prime factors in these are all of the form 3k+2, and when the binary expansions of the factors (like e.g., "101" for 5 and "111011" for 59 or "10111" for 23 and "101001" for 41) are overlaid, the resulting bit vector is always [1, 1, 1, 1, 1, 1^2], with the least significant bit-position containing 2 copies of 1's. Thus we have a(295) = a(583) = a(799) = a(943).
PROG
(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A320014(n) = v320014[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 03 2018
STATUS
approved