A004781 Binary expansion contains 3 adjacent 1's.

7, 14, 15, 23, 28, 29, 30, 31, 39, 46, 47, 55, 56, 57, 58, 59, 60, 61, 62, 63, 71, 78, 79, 87, 92, 93, 94, 95, 103, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 135, 142, 143, 151, 156, 157, 158, 159, 167

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for 2-automatic sequences.

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 24 2012

Maple

q:= n-> verify([1$3], Bits[Split](n), 'sublist'):
select(q, [$0..200])[];  # Alois P. Heinz, Oct 22 2021

Mathematica

Select[Range[200], MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {1, 1, 1}]&]  (* Harvey P. Dale, Mar 31 2011 *)
Select[Range[200], StringContainsQ[IntegerString[#, 2], "111"] &] (* Amiram Eldar, Oct 22 2021 *)
Select[Range[200], SequenceCount[IntegerDigits[#, 2], {1, 1, 1}]>0&] (* Harvey P. Dale, Dec 28 2021 *)

Prog

(Haskell)
a004781 n = a004781_list !! (n - 1)
a004781_list = filter f [0..] where
   f x | x < 7     = False
       | otherwise = (x `mod` 8) == 7 || f (x `div` 2)
-- Reinhard Zumkeller, Jun 03 2012
(PARI) is(n)=!!bitand(bitand(n, n<<1), n<<2) \\ Charles R Greathouse IV, Sep 24 2012
(Python)
from sympy import tribonacci
def A004781(n):
    def f(x):
        s = bin(x)[-1:1:-1]
        return n-1+sum(tribonacci(i+2) for i in range(len(s)) if s[i]=='1' and not '111' in s[i+1:])+('111' not in s)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jun 09 2026

Crossrefs

Complement of A003726.

Cf. A004779, A136037.

Sequence in context: A085335 A069137 A141164 * A004759 A364287 A062056

Adjacent sequences: A004778 A004779 A004780 * A004782 A004783 A004784

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

Offset corrected by Reinhard Zumkeller, Jun 03 2012

Status

approved