A364570 a(n) = A252464(n) - A364569(n), where A364569(n) is the length of the common prefix in the binary expansions of A156552(n) and n-1 [= A156552(A005940(n))].

0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 3, 0, 5, 4, 3, 0, 2, 3, 5, 0, 3, 4, 7, 0, 0, 6, 2, 5, 9, 4, 10, 0, 2, 3, 3, 4, 9, 6, 4, 0, 11, 4, 12, 5, 0, 8, 13, 0, 0, 1, 7, 7, 15, 3, 5, 6, 8, 10, 16, 5, 17, 11, 5, 0, 3, 3, 14, 4, 6, 4, 16, 5, 18, 10, 4, 7, 4, 5, 19, 0, 4, 12, 21, 5, 6, 13, 9, 6, 22, 1, 5, 9, 10, 14, 7, 0, 24, 1, 6

Offset

1,7

Links

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

Prog

(PARI)
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
A364569(n) = Abincompreflen(A156552(n), (n-1));
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A252464(n) = if(1==n, 0, (bigomega(n) + A061395(n) - 1));
A364570(n) = (A252464(n)-A364569(n));

Crossrefs

Cf. A005940, A156552, A252464, A364569, A364570, A364960 (positions of 0's).

Cf. also A347381.

Sequence in context: A092735 A035464 A194669 * A302244 A019746 A112574

Adjacent sequences: A364567 A364568 A364569 * A364571 A364572 A364573

Keyword

nonn

Author

Antti Karttunen, Aug 14 2023

Status

approved