A104176 a(n) = bitwise OR of all terms of n-th row of Pascal's triangle.

1, 1, 3, 3, 7, 15, 31, 55, 127, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 126975, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Pascal's Triangle

Formula

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.

Example

Row 0 = 1 = 1
Row 1 = 1 OR 1 = 1
Row 2 = 1 OR 2 OR 1 = 3
Row 3 = 1 OR 3 OR 3 OR 1 = 3

Mathematica

BitOr@@@Table[Binomial[n, k], {n, 0, 40}, {k, 0, n}] (* Harvey P. Dale, Jun 15 2021 *)

Prog

(PARI) a(n) = {or = binomial (n, 0); for (i=1, n, or = bitor(or, binomial(n, i)); ); return (or); } \\ Michel Marcus, Jun 08 2013

Crossrefs

Sequence in context: A056420 A030069 A004043 * A032294 A146034 A374534

Adjacent sequences: A104173 A104174 A104175 * A104177 A104178 A104179

Keyword

nonn,base,changed

Author

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

Extensions

Name changed by Franklin T. Adams-Watters, Mar 29 2014

Status

approved