A331744 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A323901(i) = A323901(j) for all i, j.

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

Offset: 1

Author

Antti Karttunen, Feb 04 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A009194(n), A323901(n)].

Links

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

Crossrefs

Cf. A002487, A009194, A163511, A323901.

Cf. also A324400, A318310, A324389, A331745, A331746, A331747.

Programs

PARI

\\ Needs also code from A323901.
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; };
A009194(n) = gcd(n, sigma(n));
Aux331744(n) = [A009194(n),A323901(n)];
v331744 = rgs_transform(vector(up_to, n, Aux331744(n)));
A331744(n) = v331744[n];

Formula

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