A323889 Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278222(i) = A278222(j), for all i, j >= 0.

1, 2, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 7, 5, 8, 2, 9, 6, 10, 4, 11, 7, 12, 3, 10, 7, 13, 5, 12, 8, 14, 2, 15, 9, 16, 6, 17, 10, 18, 4, 17, 11, 19, 7, 20, 12, 21, 3, 16, 10, 22, 7, 19, 13, 23, 5, 18, 12, 23, 8, 21, 14, 24, 2, 25, 15, 26, 9, 27, 16, 28, 6, 29, 17, 30, 10, 31, 18, 32, 4, 27, 17, 33, 11, 34, 19, 35, 7, 31, 20, 36, 12, 37, 21, 38, 3, 26, 16, 39, 10, 33, 22

Offset: 0

Author

Antti Karttunen, Feb 09 2019

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A002487(n), A278222(n)].

Links

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

Crossrefs

Cf. A002487, A278222, A286622, A324400.

Cf. also A103391, A278243, A286378, A318311, A323892, A323897 and A324533 for a "deformed variant".

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; };
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
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));
Aux323889(n) = [A002487(n), A278222(n)];
v323889 = rgs_transform(vector(1+up_to,n,Aux323889(n-1)));
A323889(n) = v323889[1+n];

Formula

a(2^n) = 2 for all n >= 0.