A335421 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335422(i)) = A046523(A335422(j)) for all i, j >= 0.
1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 6, 3, 7, 1, 8, 4, 9, 3, 10, 5, 5, 2, 10, 6, 5, 3, 8, 7, 5, 1, 11, 8, 12, 4, 13, 9, 14, 3, 15, 10, 16, 5, 10, 5, 17, 2, 15, 10, 16, 6, 10, 5, 10, 3, 18, 8, 19, 7, 3, 5, 5, 1, 20, 11, 20, 8, 21, 12, 22, 4, 22, 13, 23, 9, 8, 14, 20, 3, 22, 15, 22, 10, 24, 16, 25, 5, 26, 10, 14, 5, 20, 17, 27, 2, 22, 15, 23, 10, 10, 16, 28, 6, 26
Offset: 0
Links
Programs
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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; }; A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429 A163511(n) = if(!n,1,A005940(1+A054429(n))) A335422(n) = A005940(1+A163511(n)); v335421 = rgs_transform(vector(1+up_to,n,A046523(A335422(n-1)))); A335421(n) = v335421[1+n];
Formula
For all n >= 0, a(2^n) = 1.
Comments