A300825 Filter sequence combining A300823(n) and A300824(n).

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 9, 2, 11, 2, 12, 13, 14, 2, 15, 16, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 39, 40, 41, 42, 2, 43, 2, 44, 45, 44, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 55, 56, 2, 57, 58, 59, 2, 60, 61, 62, 63, 64, 2, 65, 66, 64, 67, 68, 69

Offset

1,2

Comments

Restricted growth sequence transform of ordered pair [A300823(n), A300824(n)].

For all i, j: a(i) = a(j) => A051953(i) = A051953(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300823(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A244042(d));
A300222(n) = (n - A244042(n));
A300824(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A300222(d));
Aux300825(n) = [A300823(n), A300824(n)];
write_to_bfile(1, rgs_transform(vector(up_to, n, Aux300825(n))), "b300825.txt");

Crossrefs

Cf. A051953, A244042, A300222, A300823, A300824.

Cf. also A293226, A300833.

Sequence in context: A323245 A323240 A300229 * A373380 A355000 A300232

Adjacent sequences: A300822 A300823 A300824 * A300826 A300827 A300828

Keyword

nonn

Author

Antti Karttunen, Mar 14 2018

Status

approved