A289282 The least significant four bytes of n! interpreted in two's complement.

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 1932053504, 1278945280, 2004310016, 2004189184, -288522240, -898433024, 109641728, -2102132736, -1195114496, -522715136, 862453760, -775946240, 2076180480, -1853882368, 1484783616, -1375731712, -1241513984, 1409286144, 738197504, -2147483648, -2147483648, 0, 0, 0

Offset

0,3

Comments

a(n) = 0 for n >= 34. - Georg Fischer, Mar 12 2019

Links

Table of n, a(n) for n=0..36.

Example

The hexadecimal column in the following list shows how the bits in the least significant four bytes are shifted to the left by each factor containing some power of 2. With two's complement the terms are negative when the highest bit is one. - Georg Fischer, Mar 13 2019
  28 -1375731712 # ae000000
  29 -1241513984 # b6000000
  30  1409286144 # 54000000
  31   738197504 # 2c000000
  32 -2147483648 # 80000000
  33 -2147483648 # 80000000
  34           0 # 00000000

Mathematica

Table[Mod[n!, 2^32] - Boole[Mod[n!, 2^32] > 2^31 - 1] * 2^32, {n, 0, 49}]

Prog

(Java) import java.math.BigInteger;
public class a289282 {
    public static void main(String[] args) {
        BigInteger pow32 = BigInteger.valueOf(2).pow(32);
        BigInteger bfact  = BigInteger.ONE;
        for (int i = 0; i < 48; i++) {
            bfact = bfact.multiply(BigInteger.valueOf(i == 0 ? 1 : i));
            System.out.println(String.valueOf(i) + " "
                + String.valueOf(bfact.mod(pow32).intValue()));
        }
    } // main
} // Georg Fischer, Mar 12 2019
(PARI) Bits = 32; N = Mod(1, 2^Bits); j = 0; until(N == 0, print1(-centerlift(-N), ", "); j += 1; N *= j); \\ Jack Brennen, Jun 30 2017
(Scala) (1 to 36).scanLeft(1)(_ * _) // Scala infers 1 and 36 are Int, which become int primitives in the Java Virtual Machine. - Alonso del Arte, Mar 02 2019
(Python)
import math
def A289282(n):
    f = math.factorial(n)
    least_four = f & 0xffffffff
    mask = 0x7fffffff
    return (least_four & mask) - (least_four & ~mask)
print([A289282(n) for n in range(37)]) # Peter Luschny, Mar 13 2019

Crossrefs

Cf. A000142, A036603.

Sequence in context: A230233 A154659 A254523 * A155456 A124355 A133942

Adjacent sequences: A289279 A289280 A289281 * A289283 A289284 A289285

Keyword

sign,easy

Author

Alonso del Arte, Jul 01 2017

Status

approved