A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 18, 3, 20, 11, 21, 6, 22, 12, 23, 2, 24, 13, 25, 7, 26, 14, 27, 4, 28, 15, 29, 8, 30, 16, 31, 1, 18, 17, 32, 9, 33, 18, 34, 5, 35, 19, 36, 10, 37, 18, 38, 3, 39, 20, 40, 11, 25, 21, 41, 6, 12, 22, 18, 12, 17, 23, 42, 2, 43, 24, 44, 13, 45, 25, 46, 7, 47

Offset: 1

Author

Antti Karttunen, Aug 10 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A007733(n), A336158(n)].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A007733, A336158, A336933, A336935, A336936.

Programs

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
Aux336934(n) = [A007733(n), A336158(n)];
v336934 = rgs_transform(vector(up_to, n, Aux336934(n)));
A336934(n) = v336934[n];