A322822 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(2) = -1, f(n) = 0 if n is a Fermi-Dirac prime (A050376) > 2, and f(n) = A300840(n) for all other numbers.

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

Offset: 1

Author

Antti Karttunen, Dec 29 2018

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A322823(i) = A322823(j).

Links

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

Crossrefs

Cf. A050376, A052330, A052331, A302777, A300840, A322823.

Cf. also A322805, A322807.

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; };
ispow2(n) = (n && !bitand(n,n-1));
A302777(n) = ispow2(isprimepower(n));
A050376list(up_to) = { my(v=vector(up_to), i=0); for(n=1,oo,if(A302777(n), i++; v[i] = n); if(i == up_to,return(v))); };
v050376 = A050376list(up_to);
A050376(n) = v050376[n];
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A300840(n) = A052330(A052331(n)>>1);
A322822aux(n) = if((2==n),-1,if(A302777(n),0,A300840(n)));
v322822 = rgs_transform(vector(up_to,n,A322822aux(n)));
A322822(n) = v322822[n];