A141032 -id:A141032 - cp's OEIS frontend

A141060 Fourth quadrisection of Jacobsthal numbers A001045: a(n)=16a(n-1)-5.

3, 43, 683, 10923, 174763, 2796203, 44739243, 715827883, 11453246123, 183251937963, 2932031007403, 46912496118443, 750599937895083, 12009599006321323, 192153584101141163, 3074457345618258603, 49191317529892137643

Offset: 0

Paul Curtz, Jul 30 2008

Jacobsthal numbers ending with the decimal digit 3. - Jianing Song, Aug 30 2022

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (17,-16).

The other quadrisections of A001045 are A195156 (first), A139792 (second), and A144864 (third).

[(1/3)*(1+8*16^n): n in [0..25]]; // Vincenzo Librandi, May 25 2011

LinearRecurrence[{17,-16},{3,43},30] (* Harvey P. Dale, Mar 16 2015 *)

a(n)=8*16^n\3+1 \\ Charles R Greathouse IV, May 25 2011

def A141060(n): return ((1<<(n<<2)+3)|1)//3 # Chai Wah Wu, Apr 18 2025

a(n) = A139792(n) + A013776(n).
a(n+1) - a(n) = 10*A013709(n) = 40*A001025(n).
G.f.: (3-8*x)/((1-x)*(1-16*x)). [Colin Barker, Apr 05 2012]
a(0)=3, a(1)=43, a(n)=17*a(n-1)-16*a(n-2). - Harvey P. Dale, Mar 16 2015
From Jianing Song, Aug 30 2022: (Start)
a(n) = A001045(4*n+3).
a(n) = 10*A141032(n) + 3 = 20*A098704(n+1) + 1 = 40*A131865(n-1) + 1 for n >= 1. (End)

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

A141060 Fourth quadrisection of Jacobsthal numbers A001045: a(n)=16a(n-1)-5.

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