A387412 The length of the maximal common prefix of the binary expansions of n and A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 3, 5, 2, 1, 1, 2, 1, 1, 4, 3, 2, 2, 3, 2, 1, 1, 5, 1, 3, 1, 2, 3, 2, 3, 4, 4, 3, 1, 3, 3, 1, 4, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 3, 1, 1, 2, 1, 2, 1, 1, 4, 2, 3, 1, 3, 2, 4, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 4, 2, 6, 2, 3, 1, 4, 1, 1, 3, 5, 1, 3, 2, 3

Offset

1,4

Links

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

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to prime indices in the factorization of n.

Formula

a(n) = (1+A000523(n)) - A387413(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A387412(n) = { my(a=binary(n), b=binary(A003961(n)), i=1); while(i<=#a, if(a[i]!=b[i], return(i-1)); i++); (#a); };
(Python)
from os.path import commonprefix
from math import prod
from sympy import factorint, nextprime
def A387412(n): return len(commonprefix([bin(n)[2:], bin(prod(nextprime(p)**e for p, e in factorint(n).items()))[2:]])) # Chai Wah Wu, Sep 03 2025

Crossrefs

Cf. A000523, A003961, A387413.

Cf. also A387422.

Sequence in context: A243977 A328569 A377514 * A016569 A072801 A098872

Adjacent sequences: A387409 A387410 A387411 * A387413 A387414 A387415

Keyword

nonn

Author

Antti Karttunen, Sep 01 2025

Status

approved