A322823 - OEIS

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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)).

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

(list; graph; refs; listen; history; text; internal format)

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

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

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

Cf. A050376, A052330, A052331, A302777, A300840, A322822.

Sequence in context: A180160 A101661 A322989 * A334872 A263844 A079644

Adjacent sequences: A322820 A322821 A322822 * A322824 A322825 A322826

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 29 2018

STATUS

approved