A351034 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351032(i) = A351032(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jan 29 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of A351032.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A019565, A048673, A289814, A291759, A351030, A351032, A351033.

Cf. also A293224.

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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A351032(n) = { my(m=1); fordiv(n,d,if(dA019565(A291759(d)))); (m); };
v351034 = rgs_transform(vector(up_to, n, A351032(n)));
A351034(n) = v351034[n];