A351093 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j), for all i, j >= 1.

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 5, 2, 6, 3, 7, 1, 5, 4, 3, 2, 8, 5, 2, 2, 9, 6, 10, 3, 11, 7, 12, 1, 10, 5, 12, 4, 13, 3, 14, 2, 10, 8, 13, 5, 15, 2, 11, 2, 16, 9, 10, 6, 11, 10, 6, 3, 8, 11, 2, 7, 3, 12, 17, 1, 17, 10, 6, 5, 7, 12, 5, 4, 3, 13, 18, 3, 6, 14, 3, 2, 19, 10, 20, 8, 21, 13, 22, 5, 20, 15, 23, 2, 24, 11

Offset: 1

Author

Antti Karttunen, Jan 31 2022

Keywords

• nonn
• easy
• look

Comments

Restricted growth sequence transform of A351091.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A351090, A351091, A351094.

Programs

PARI

up_to = 20000;
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); };
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); }; \\ From A289813
A351091(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289813(d))); (m); };
v351093 = rgs_transform(vector(up_to, n, A351091(n)));
A351093(n) = v351093[n];