A387424 Partial sums of A387423.

0, 1, 2, 4, 6, 6, 8, 11, 14, 16, 19, 21, 23, 25, 27, 31, 33, 34, 37, 38, 41, 44, 48, 51, 54, 58, 62, 62, 64, 68, 72, 77, 82, 87, 92, 96, 98, 103, 108, 111, 113, 118, 121, 124, 128, 132, 137, 141, 145, 150, 155, 158, 160, 164, 169, 172, 177, 182, 185, 190, 192, 196, 200, 206, 211, 215, 218, 224, 230, 234, 238, 244

Offset: 1

Author

Antti Karttunen, Sep 01 2025

Keywords

• nonn
• base
• new

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).

Crossrefs

Cf. A000203, A387423.

Cf. also A387425.

Programs

PARI

up_to = 65537;
A387423(n) = { my(a=binary(n), b=binary(sigma(n)), i=1); while(i<=#a,if(a[i]!=b[i],return(#a-(i-1))); i++); (0); };
A387424list(up_to) = { my(v=vector(up_to)); v[1] = 0; for(n=2,up_to,v[n] = v[n-1]+A387423(n)); (v); };
v387424 = A387424list(up_to);
A387424(n) = v387424[n];

Formula

a(1) = 0; for n > 1, a(n) = a(n-1) + A387423(n).