A324346 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A324055(i) = A324055(j), for all i, j >= 0.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 21, 22, 2, 27, 28, 29, 5, 30, 19, 18, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 2, 55, 56, 18, 15, 57, 19, 58, 59, 60, 61, 62, 63, 64, 65, 32, 66, 67, 68, 69, 63, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset: 0

Author

Antti Karttunen, Feb 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A005811(n), A324055(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005811, A324055, A324345, A324347.

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; };
A005811(n) = hammingweight(bitxor(n, n>>1)); \\ From A005811
A324055(n) = { my(m1=2,m2=1,p=2,mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4),mp *= p,m2 *= (mp-1)/(p-1))); n>>=1); (m1-m2); };
Aux324346(n) = [A005811(n), A324055(n)];
v324346 = rgs_transform(vector(1+up_to,n,Aux324346(n-1)));
A324346(n) = v324346[1+n];

Formula

For all n >= 1, a((2^n)-1) = 2.