A361021 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Mar 03 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of the triplet [A007814(n), A001065(n), A051953(n)].

For all i, j >= 1:

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A305895(i) = A305895(j),

a(i) = a(j) => A319346(i) = A319346(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A001065, A007814, A051953.

Cf. A305801, A305895, A319346.

Cf. also A353560.

Differs from A353520 for the first time at n=254, where a(254) = 187, while A353520(254) = 125.

Programs

PARI

up_to = 100000;
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; };
A007814(n) = valuation(n,2);
A001065(n) = (sigma(n)-n);
A051953(n) = (n-eulerphi(n));
Aux361021(n) = [A007814(n), A001065(n), A051953(n)];
v361021 = rgs_transform(vector(up_to,n,Aux361021(n)));
A361021(n) = v361021[n];