A323892 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A033879(i) = A033879(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Feb 09 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A002487(n), A033879(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A033879.

Cf. also A318310, A323889.

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
A033879(n) = (2*n-sigma(n));
A323892aux(n) = [A002487(n), A033879(n)];
v323892 = rgs_transform(vector(up_to,n,A323892aux(n)));
A323892(n) = v323892[n];

Formula

a(2^n) = 1 for all n >= 0.