A163617 -id:A163617 - cp's OEIS frontend

A178897 a(n) = n OR 10n, where OR is bitwise OR.

0, 11, 22, 31, 44, 55, 62, 71, 88, 91, 110, 111, 124, 143, 142, 159, 176, 187, 182, 191, 220, 215, 222, 247, 248, 251, 286, 287, 284, 319, 318, 319, 352, 363, 374, 383, 364, 375, 382, 423, 440, 443, 430, 431, 444, 495, 494, 511, 496, 507, 502, 511, 572, 567

Offset: 0

Dmitry Kamenetsky, Jun 21 2010

nonn

Cf. A163617, A178890, A178891, A178892, A178893, A178894, A178895, A178896.

f[n_] := BitOr[n, 10n]; Array[f, 54, 0] (* Robert G. Wilson v, Jun 28 2010 *)

More terms from Robert G. Wilson v, Jun 28 2010

A328105 Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).

Original entry on oeis.org

2, 4, 5, 8, 7, 12, 9, 15, 11, 17, 17, 20, 19, 26, 21, 29, 22, 27, 30, 33, 30, 34, 37, 40, 37, 39, 41, 49, 44, 49, 48, 53, 41, 56, 49, 64, 50, 62, 59, 66, 64, 60, 66, 69, 61, 77, 65, 73, 67, 74, 70, 89, 78, 87, 78, 94, 85, 88, 89, 100, 91, 101, 95, 110, 92, 85, 98, 102, 102, 102, 115, 109, 101, 105, 121, 118, 121, 129

Offset: 0

Antti Karttunen, Oct 05 2019

nonn

Cf. A000120, A110240, A163617, A269160, A328104.

Cf. also A070952, A328106, A328107, A328108, A328109.

A269160(n) = bitxor(n, bitor(2*n, 4*n));
A110240(n) = if(!n,1,A269160(A110240(n-1)));
A163617(n) = bitor(n,n<<1);
A328105(n) = hammingweight(A163617(A110240(n)));
\\ Use this one for writing b-files:
A328105write(up_to) = { my(s=1, n=0); for(n=0,up_to, write("b328105.txt", n, " ", hammingweight(bitor(s, s<<1))); s = A269160(s)); };

a(n) = A000120(A328104(n)) = A000120(A163617(A110240(n))).

For all n >= 0, A070952(a) < a(n) <= 2*A070952(n).

A163618 a(2n) = 2 a(n). a(2n - 1) = 2 a(n) - 2 - (-1)^n, for all n in Z.

Original entry on oeis.org

0, 1, 2, 1, 4, 1, 2, 5, 8, 1, 2, 1, 4, 9, 10, 13, 16, 1, 2, 1, 4, 1, 2, 5, 8, 17, 18, 17, 20, 25, 26, 29, 32, 1, 2, 1, 4, 1, 2, 5, 8, 1, 2, 1, 4, 9, 10, 13, 16, 33, 34, 33, 36, 33, 34, 37, 40, 49, 50, 49, 52, 57, 58, 61, 64, 1, 2, 1, 4, 1, 2, 5, 8, 1, 2, 1, 4, 9, 10, 13, 16, 1, 2, 1, 4, 1, 2, 5, 8, 17

Offset: 0

Michael Somos, Aug 01 2009

nonn

Integers n>=0 such that a(n) = 1 is A118113.

Fibbinary numbers (A003714) give all integers n>=0 for which a(n+1) = 1 or 2. - Michael Somos, Feb 21 2016

			G.f. = x + 2*x^2 + x^3 + 4*x^4 + x^5 + 2*x^6 + 5*x^7 + 8*x^8 + x^9 + 2*x^10 + ...

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A163617.

Table[(-1)*BitOr[-n, -2*n], {n, 0, 50}] (* G. C. Greubel, Jul 30 2017 *)

PARI
```
{a(n) = n=-n; -bitor(n, n<<1)};
```

{a(n) = if( n==0 || n==1, n, 2 * a((n+1) \ 2) - (n%2) * (2 + (-1)^((n+1) \ 2)))};

a(n) = -A163617(-n) for all n in Z.

A269170 a(n) = n OR floor(n/2), where OR is bitwise-OR (A003986).

Original entry on oeis.org

0, 1, 3, 3, 6, 7, 7, 7, 12, 13, 15, 15, 14, 15, 15, 15, 24, 25, 27, 27, 30, 31, 31, 31, 28, 29, 31, 31, 30, 31, 31, 31, 48, 49, 51, 51, 54, 55, 55, 55, 60, 61, 63, 63, 62, 63, 63, 63, 56, 57, 59, 59, 62, 63, 63, 63, 60, 61, 63, 63, 62, 63, 63, 63, 96, 97, 99, 99, 102, 103, 103, 103, 108, 109, 111, 111, 110, 111

Offset: 0

Antti Karttunen, Feb 22 2016

Fibbinary numbers (A003714) give all integers n >= 0 for which a(n) = A003188(n) and also for which a(n) = A032766(n).

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A000035, A003714, A003986.
Cf. A163617 (even bisection).
Cf. also A003188, A048735, A032766.

Table[BitOr[n, Quotient[n, 2]], {n, 0, 127}] (* Paolo Xausa, Aug 26 2025 *)

a(n) = bitor(n, n\2); \\ Michel Marcus, Feb 29 2016

def A269170(n): return n| n>>1 # Chai Wah Wu, Jun 29 2022

(define (A269170 n) (A003986bi n (/ (- n (A000035 n)) 2))) ;; Here A003986bi implements dyadic bitwise-OR operation (see A003986).

a(n) = A003986(n,(n-A000035(n))/2).
Other identities and observations. For all n >= 0:
a(2n) = A163617(n).
A003188(n) <= a(n) <= A032766(n).

A334076 a(n) = bitwise NOR of n and 2n.

Original entry on oeis.org

0, 0, 1, 0, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 15, 12, 9, 8, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 31, 28, 25, 24, 19, 16, 17, 16, 7, 4, 1, 0, 3, 0, 1, 0, 15, 12, 9, 8, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 63, 60, 57, 56, 51, 48, 49, 48, 39, 36, 33, 32, 35, 32, 33

Offset: 0

Alois P. Heinz, Apr 13 2020

Exactly all bits that are 0 in both parameters (but not a leading 0 of both) are set to 1 in the output of bitwise NOR.

Alois P. Heinz, Table of n, a(n) for n = 0..32767
Wikipedia, Bitwise operation

Cf. A000079, A048724, A125835, A141032, A163617, A213370, A247648.

a:= n-> Bits[Nor](n, 2*n):
seq(a(n), n=0..127);

a(n) = my(x=bitor(n, 2*n)); bitneg(x, #binary(x)); \\ Michel Marcus, Apr 14 2020

def A334076(n):
    m = n|(2*n)
    return 0 if n == 0 else 2**(len(bin(m))-2)-1-m # Chai Wah Wu, Apr 14 2020

a(n) = 0 <=> n in { A247648 } union { 0 }.
a(n) = n-1 <=> n in { A000079 }.
a(n) = n/2 <=> n in { A125835 }.
a(n) = n*3/4 <=> n in { A141032 }.

cp's OEIS Frontend

A178897 a(n) = n OR 10n, where OR is bitwise OR.

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A328105 Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).

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A163618 a(2*n) = 2 * a(n). a(2*n - 1) = 2 * a(n) - 2 - (-1)^n, for all n in Z.

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A269170 a(n) = n OR floor(n/2), where OR is bitwise-OR (A003986).

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A334076 a(n) = bitwise NOR of n and 2n.

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A163618 a(2n) = 2 a(n). a(2n - 1) = 2 a(n) - 2 - (-1)^n, for all n in Z.