A364577 Lexicographically earliest infinite sequence such that a(i) = a(j) => A294898(i) = A294898(j) and A329697(i) = A329697(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Aug 12 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A294898(n), A329697(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000203, A005187, A294898, A329697.

Cf. also A318311, A336473.

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; };
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A294898(n) = (A005187(n)-sigma(n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));Aux364577(n) = [A294898(n), A329697(n)];
v364577 = rgs_transform(vector(up_to, n, Aux364577(n)));
A364577(n) = v364577[n];