A336156 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A336158(i) = A336158(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A007814(1+n), A336158(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.

For all i, j: A324400(i) = A324400(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000265, A007814, A046523, A336158.

Cf. also A324400, A336152, A336153, A336154, A336155.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A007814(n) = valuation(n,2);
Aux336156(n) = [A007814(1+n), A336158(n)];
v336156 = rgs_transform(vector(up_to, n, Aux336156(n)));
A336156(n) = v336156[n];