A336154 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A278222(i) = A278222(j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 4, 7, 8, 5, 9, 10, 11, 2, 4, 7, 8, 7, 12, 13, 14, 5, 9, 13, 15, 10, 16, 17, 18, 2, 4, 7, 8, 7, 12, 13, 14, 7, 12, 19, 20, 13, 21, 22, 23, 5, 9, 13, 15, 13, 21, 24, 25, 10, 16, 22, 26, 17, 27, 28, 29, 2, 4, 7, 8, 7, 12, 13, 14, 7, 12, 19, 20, 13, 21, 22, 23, 7, 12, 19, 20, 19, 30, 31, 32, 13, 21, 31, 33, 22, 34, 35, 36, 5, 9, 13, 15, 13, 21, 24, 25, 13, 21

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A007814(1+n), A278222(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
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007814, A278222.

Cf. also A286622, A324400, A336153, A336155, A336156.

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; };
A007814(n) = valuation(n,2);
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));
Aux336154(n) = [A007814(1+n), A278222(n)];
v336154 = rgs_transform(vector(up_to, n, Aux336154(n)));
A336154(n) = v336154[n];