A336155 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A335915(i) = A335915(j), for all i, j >= 1.

1, 2, 3, 2, 4, 2, 5, 2, 1, 6, 7, 2, 8, 6, 9, 2, 10, 2, 11, 6, 4, 12, 13, 2, 10, 14, 3, 6, 15, 6, 16, 2, 17, 18, 19, 2, 20, 21, 22, 6, 15, 6, 23, 12, 4, 24, 25, 2, 10, 18, 19, 14, 26, 2, 27, 6, 28, 29, 30, 6, 31, 12, 32, 2, 33, 12, 34, 18, 35, 18, 36, 2, 37, 38, 19, 21, 28, 14, 39, 6, 1, 29, 40, 6, 41, 42, 43, 12, 44, 6, 45, 24, 17, 46, 47, 2, 48, 18, 7, 18, 49, 18, 50, 14, 10

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A007814(1+n), A335915(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, A335915.

Cf. also A324400, A336154, A336156, A336162.

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);
A000265(n) = (n>>valuation(n,2));
A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
Aux336155(n) = [A007814(1+n), A335915(n)];
v336155 = rgs_transform(vector(up_to, n, Aux336155(n)));
A336155(n) = v336155[n];