A356320 Length of the common prefix in binary expansions of n and A332221(n) = A156552(sigma(A005940(1+n))).

0, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 4, 3, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 6, 1, 2, 3, 2, 3, 1, 3, 2, 2, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 3, 3, 1, 4, 2, 3, 1, 1, 3, 3, 3, 6, 3, 2, 1, 3, 2, 1, 1, 2, 3, 2, 2, 2, 2, 2, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Antti Karttunen, Aug 06 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32759
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A005940, A070939, A156552, A324054, A347380, A356321, A332222.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
Abincompreflen(n, m) = { my(x=binary(n),y=binary(m),u=min(#x,#y)); for(i=1,u,if(x[i]!=y[i],return(i-1))); (u);};
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A347380(n) = Abincompreflen(A156552(n), A156552(sigma(n)));
A356320(n) = A347380(A005940(1+n));
\\ Alternatively as:
A356320(n) = Abincompreflen(n, A156552(sigma(A005940(1+n))));