A378522 Lexicographically earliest infinite sequence such that a(i) = a(j) => A378518(i) = A378518(j), for all i, j >= 1.

1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 1, 5, 1, 1, 1, 6, 1, 7, 1, 8, 1, 1, 1, 9, 10, 1, 11, 5, 1, 1, 1, 12, 1, 1, 1, 13, 1, 1, 1, 14, 1, 1, 1, 6, 15, 1, 1, 16, 15, 17, 1, 18, 1, 19, 1, 9, 1, 1, 1, 20, 1, 1, 21, 22, 1, 1, 1, 23, 1, 1, 1, 24, 1, 1, 25, 26, 1, 1, 1, 27, 28, 1, 1, 22, 1, 1, 1, 12, 1, 29, 1, 30, 1, 1, 1, 31, 1, 29, 32, 33, 1, 1, 1, 34, 1

Offset: 1

Author

Antti Karttunen, Nov 30 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of A378518.

Links

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

Crossrefs

Cf. A005117 (positions of 1's), A097248, A378518.

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; };
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };
A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };
A378518(n) = (n - A097248(n));
v378522 = rgs_transform(vector(up_to, n, A378518(n)));
A378522(n) = v378522[n];