A387407 Partial sums of A387422, where A387422 is the length of the maximal common prefix of the binary expansions of n and sigma(n).

1, 2, 3, 4, 5, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22, 23, 26, 30, 32, 36, 38, 40, 41, 43, 45, 46, 47, 52, 55, 56, 57, 58, 59, 60, 61, 63, 67, 68, 69, 72, 76, 77, 80, 83, 85, 87, 88, 90, 92, 93, 94, 97, 101, 103, 104, 107, 108, 109, 112, 113, 117, 119, 121, 122, 124, 127, 131, 132, 133, 136, 139, 140, 145, 146, 147

Offset

1,2

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 sigma(n).

Formula

a(1) = 1; and for n > 1, a(n) = a(n-1) + A387422(n).

a(n) = A387408(n) + A387409(n).

Prog

(PARI)
up_to = 65537;
A387422(n) = { my(a=binary(n), b=binary(sigma(n)), i=1); while(i<=#a, if(a[i]!=b[i], return(i-1)); i++); (#a); };
A387407list(up_to) = { my(v=vector(up_to)); v[1] = A387422(1); for(n=2, up_to, v[n] = v[n-1]+A387422(n)); (v); };
v387407 = A387407list(up_to);
A387407(n) = v387407[n];

Crossrefs

Cf. A003961, A387422, A387408, A387409.

Cf. also A387424.

Sequence in context: A047369 A389734 A004827 * A155941 A378844 A046892

Adjacent sequences: A387404 A387405 A387406 * A387408 A387409 A387410

Keyword

nonn

Author

Antti Karttunen, Sep 03 2025

Status

approved