A322023 Lexicographically earliest such sequence a that a(i) = a(j) => A081373(i) = A081373(j) and A303756(i) = A303756(j), for all i, j. Here A081373 and A303756 are the ordinal transforms of Euler phi and Carmichael lambda.

1, 2, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 1, 3, 7, 4, 1, 8, 1, 9, 10, 2, 1, 11, 1, 5, 2, 11, 1, 12, 1, 13, 14, 5, 7, 15, 1, 3, 4, 16, 1, 17, 1, 18, 9, 2, 1, 19, 2, 20, 7, 11, 1, 8, 14, 21, 10, 2, 1, 22, 1, 2, 23, 4, 24, 25, 1, 9, 7, 17, 1, 26, 1, 20, 18, 12, 14, 27, 1, 28, 1, 20, 1, 29, 30, 3, 7, 12, 1, 31, 32, 4, 18, 2, 3, 33, 1, 8, 6, 34, 1, 35, 1, 36, 37

Offset: 1

Author

Antti Karttunen, Nov 29 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A081373(n), A303756(n)].

Links

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

Crossrefs

Cf. A000010, A002322, A081373, A303756, A319339, A322024, A322025 (ordinal transform).

Programs

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
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; };
A002322(n) = lcm(znstar(n)[2]); \\ From A002322
v081373 = ordinal_transform(vector(up_to,n,eulerphi(n)));
A081373(n) = v081373[n];
v303756 = ordinal_transform(vector(up_to,n,A002322(n)));
A303756(n) = v303756[n];
v322023 = rgs_transform(vector(up_to, n, [A081373(n), A303756(n)]));
A322023(n) = v322023[n];