A387413 The length of binary expansion of n minus 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).

0, 1, 1, 0, 2, 1, 2, 3, 3, 0, 3, 3, 3, 3, 3, 3, 2, 0, 3, 4, 4, 3, 4, 4, 1, 2, 3, 3, 2, 3, 4, 5, 1, 5, 3, 5, 4, 3, 4, 3, 2, 2, 3, 5, 3, 3, 5, 2, 4, 5, 5, 5, 4, 5, 5, 5, 0, 5, 3, 5, 5, 4, 5, 5, 6, 6, 3, 5, 4, 6, 4, 5, 3, 6, 6, 6, 4, 6, 5, 5, 5, 5, 4, 6, 5, 5, 5, 4, 6, 5, 3, 5, 1, 5, 4, 6, 3, 6, 6, 4, 2, 6, 4, 5, 4

Offset

1,5

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)) - A387412(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A387413(n) = { my(a=binary(n), b=binary(A003961(n)), i=1); while(i<=#a, if(a[i]!=b[i], return(#a-(i-1))); i++); (0); };

Crossrefs

Cf. A000523, A003961, A387412, A387414 (positions of 0's).

Cf. also A387423.

Sequence in context: A107853 A054758 A077876 * A095056 A337557 A186333

Adjacent sequences: A387410 A387411 A387412 * A387414 A387415 A387416

Keyword

nonn

Author

Antti Karttunen, Sep 01 2025

Status

approved