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A322823
a(n) = 0 if n is 1 or a Fermi-Dirac prime (A050376), otherwise a(n) = 1 + a(A300840(n)).
3
0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 2, 0, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 2, 3, 0, 2, 0, 1, 2, 1, 4, 3, 0, 1, 2, 3, 0, 2, 0, 3, 4, 1, 0, 2, 0, 1, 2, 3, 0, 2, 4, 3, 2, 1, 0, 3, 0, 1, 5, 3, 4, 2, 0, 3, 2, 4, 0, 3, 0, 1, 2, 3, 5, 2, 0, 4, 0, 1, 0, 3, 4, 1, 2, 3, 0, 4, 5, 3, 2, 1, 4, 2, 0, 1, 6, 3, 0, 2, 0, 3, 4
OFFSET
1,12
COMMENTS
For n > 1, a(n) gives the number of edges needed to traverse from n to reach the leftmost branch (where the terms of A050376 are located) in the binary tree illustrated in A052330.
LINKS
FORMULA
a(1) = 0; for n > 1, if A302777(n) == 1, a(n) = 0, otherwise a(n) = 1 + a(A300840(n)).
PROG
(PARI)
up_to = 10000;
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);
A322823(n) = if((1==n)||(1==A302777(n)), 0, 1+A322823(A300840(n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 29 2018
STATUS
approved