A329048 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329038(i) = A329038(j) for all i, j.

1, 2, 2, 3, 4, 5, 2, 6, 3, 7, 8, 9, 4, 10, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 26, 6, 27, 28, 29, 3, 30, 7, 31, 32, 33, 8, 34, 9, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 4, 50, 10, 51, 52, 53, 5, 54, 11, 55, 56, 57, 12, 58, 13, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 14, 74, 15, 75, 76, 77, 16

Offset: 0

Author

Antti Karttunen, Nov 11 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A329038, i.e., of function f(n) = A246277(A276086(n)).

For all i, j:

a(i) = a(j) => A286626(i) = A286626(j),

a(i) = a(j) => A276088(i) = A276088(j),

a(i) = a(j) => A276153(i) = A276153(j),

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768

Crossrefs

Cf. A046523, A246277, A276086, A276088, A276153, A278226, A286626, A329038.

Cf. also A329345.

Programs

PARI

up_to = 32768;
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; };
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329038(n) = A246277(A276086(n));
v329048 = rgs_transform(vector(1+up_to, n, A329038(n-1)));
A329048(n) = v329048[1+n];