A324343 Lexicographically earliest positive sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A324342(i) = A324342(j), for all i, j >= 0.

1, 2, 2, 3, 2, 4, 5, 6, 2, 4, 7, 8, 9, 10, 11, 12, 2, 4, 7, 13, 7, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 2, 4, 7, 13, 25, 14, 18, 22, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 2, 4, 7, 13, 50, 51, 52, 53, 50, 54, 55, 56, 38, 39, 57, 58, 59, 60, 55, 56, 61, 62, 63, 64, 19, 65, 66, 67, 16, 68, 69, 70, 71, 72, 73, 74, 75, 63, 76

Offset: 0

Author

Antti Karttunen, Feb 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A324342(n)], or equally, of [A286622(n), A324342(n)].

For all i, j: a(i) = a(j) => A324344(i) = A324344(j).

Links

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

Crossrefs

Cf. A278222, A286622, A324342, A324344.

Cf. also A323889, A324345.

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));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
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));
A324343aux(n) = [A278222(n), A324342(n)];
v324343 = rgs_transform(vector(1+up_to,n,A324343aux(n-1)));
A324343(n) = v324343[1+n];