A175481 a(1)=1 and a(n+1) = Sum_{k=1..n} b(n,a(k)), where b(n,a(k)) is the largest positive integer that, when written in binary, occurs as a substring in both binary n and binary a(k).

1, 1, 2, 3, 5, 10, 11, 11, 13, 15, 36, 49, 42, 56, 54, 47, 42, 53, 52, 57, 112, 129, 131, 136, 163, 137, 183, 196, 198, 192, 162, 109, 218, 172, 275, 273, 151, 213, 196, 181, 343, 285, 367, 395, 437, 549, 389, 403, 524, 645, 409, 418, 568, 632, 608, 587, 719, 576, 570, 599, 565, 533, 393, 255, 595, 569, 565, 494, 984, 819

Offset

1,3

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..2048

Prog

(Python)
from itertools import count
def b(n, ak):
    for x in count(0):
        bx = bin(min(n, ak)-x)[2:]
        if bx in bin(n)[2:] and bx in bin(ak)[2:]:
            return(int(bx, 2)); break
def A175481_list(nmax):
    A = [1]
    for n in range(2, nmax+1):
        A.append((sum(b(n-1, A[k-1]) for k in range(1, n))))
    return(A) # John Tyler Rascoe, Dec 29 2023

Crossrefs

Sequence in context: A286144 A038807 A094542 * A288244 A246392 A219860

Adjacent sequences: A175478 A175479 A175480 * A175482 A175483 A175484

Keyword

base,nonn

Author

Leroy Quet, May 26 2010

Extensions

More terms from Sean A. Irvine, Mar 02 2011

Status

approved