A324344 Lexicographically earliest positive sequence such that a(i) = a(j) => A000120(i) = A000120(j) and A324342(i) = A324342(j), for all i, j >= 0.

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

Offset: 0

Author

Antti Karttunen, Feb 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A000120(n), A324342(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A000120, A324342, A324343.

Cf. also A318310.

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; };
A002110(n) = prod(i=1,n,prime(i));
A030308(n,k) = bittest(n,k);
A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A324342(n) = A276150(A283477(n));
A324344aux(n) = [hammingweight(n), A324342(n)];
v324344 = rgs_transform(vector(1+up_to,n,A324344aux(n-1)));
A324344(n) = v324344[1+n];