511 (number)

← 510 511 512 →
List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	five hundred eleven
Ordinal	511th; (five hundred eleventh)
Factorization	7 × 73
Greek numeral	ΦΙΑ´
Roman numeral	DXI, dxi
Binary	1111111112
Ternary	2002213
Senary	22116
Octal	7778
Duodecimal	36712
Hexadecimal	1FF16

511 is the natural number following 510 and preceding 512.

In mathematics

It is a Mersenne number, being one less than a power of 2: $511=2^{9}-1$ .^[1] As a result, 511 is a palindromic number and a repdigit in bases 2 (111111111₂). It is also palindromic and a repdigit in base 8 (777₈).

It is a generalized heptagonal number (sequence A085787 in the OEIS), since $511={\frac {1}{2}}(5n^{2}-3n)$ when $n=-14$ .

It is a Harshad number^[2] in bases 3, 5, 7, 10, 13 and 15.

Special use in computers

The octal representation of 511 (777₈) is commonly used by Unix commands to specify a custom record separator in order to "slurp" input as a whole, rather than line-by-line (i.e. separated at newline characters).^[3]

References

↑ Weisstein, Eric W. "Mersenne Number". MathWorld--A Wolfram Web Resource. Retrieved 9 December 2024.
↑ Sloane, N. J. A. (ed.). "Sequence A154701 (Numbers k such that k, k + 1 and k + 2 are 3 consecutive Harshad numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
↑ "Official Count to 1 Trillion Thread".

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[1] Weisstein, Eric W. "Mersenne Number". MathWorld--A Wolfram Web Resource. Retrieved 9 December 2024.

[2] Sloane, N. J. A. (ed.). "Sequence A154701 (Numbers k such that k, k + 1 and k + 2 are 3 consecutive Harshad numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[3] "Official Count to 1 Trillion Thread".

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