A104176 - OEIS

A104176

a(n) = bitwise OR of all terms of n-th row of Pascal's triangle.

%I #13 Jun 15 2021 11:18:57

%S 1,1,3,3,7,15,31,55,127,127,255,511,1023,2047,4095,8191,16383,32767,

%T 65535,126975,262143,524287,1048575,2097151,4194303,8388607,16777215,

%U 33554431,67108863,134217727,268435455,536870911,1073741823,2147483647

%N a(n) = bitwise OR of all terms of n-th row of Pascal's triangle.

%H Harvey P. Dale, <a href="/A104176/b104176.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>

%F Most but not all terms are of the form 2^n - 1 for some integer n. In the first 1600 terms we have: repeated numbers: 1, 3, 127 and 274877906943. Numbers not of form 2^n -1: 55, 126975.

%e Row 0 = 1 = 1

%e Row 1 = 1 OR 1 = 1

%e Row 2 = 1 OR 2 OR 1 = 3

%e Row 3 = 1 OR 3 OR 3 OR 1 = 3

%t BitOr@@@Table[Binomial[n,k],{n,0,40},{k,0,n}] (* _Harvey P. Dale_, Jun 15 2021 *)

%o (PARI) a(n) = {or = binomial (n, 0); for (i=1, n, or = bitor(or, binomial(n, i));); return (or);} \\ _Michel Marcus_, Jun 08 2013

%K nonn,base

%O 0,3

%A Andrew G. West (WestA(AT)wlu.edu), Mar 28 2005

%E Name changed by _Franklin T. Adams-Watters_, Mar 29 2014