A323897 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A083254(i) = A083254(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Feb 09 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A002487(n), A083254(n)].

Links

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

Crossrefs

Cf. A000010, A002487, A083254.

Cf. also A323892, A323898.

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
A083254(n) = (2*eulerphi(n)-n);
A323897aux(n) = [A002487(n), A083254(n)];
v323897 = rgs_transform(vector(up_to,n,A323897aux(n)));
A323897(n) = v323897[n];

Formula

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