A175824 -id:A175824 - cp's OEIS frontend

A175825 Maximum signed integer that can be stored in n bytes.

127, 32767, 8388607, 2147483647, 549755813887, 140737488355327, 36028797018963967, 9223372036854775807, 2361183241434822606847, 604462909807314587353087, 154742504910672534362390527, 39614081257132168796771975167, 10141204801825835211973625643007

Offset: 1

Grant Garcia, Sep 14 2010

			a(1) = 2^7 - 1 = 128 - 1 = 127.
a(2) = 2^15 - 1 = 32768 - 1 = 32767.
a(3) = 2^23 - 1 = 8388608 - 1 = 8388607.

Colin Barker, Table of n, a(n) for n = 1..400
Wikipedia, Byte
Index entries for linear recurrences with constant coefficients, signature (257,-256).

Cf. A000225, A175824.

Mathematica
```
Table[2^(8n - 1) - 1, {n, 1, 11}]
```

Vec(x*(127+128*x)/((1-x)*(1-256*x)) + O(x^50)) \\ Colin Barker, May 12 2016

print([2**(8 * i - 1) - 1 for i in range(1, 12)])

a(n) = 2^(8*n - 1) - 1.
From Colin Barker, May 12 2016: (Start)
a(n) = 257*a(n-1)-256*a(n-2) for n>2.
G.f.: x*(127+128*x) / ((1-x)*(1-256*x)).
(End)

A295838 Largest value corresponding to a string of n printable ASCII characters.

Original entry on oeis.org

0, 126, 32382, 8289918, 2122219134, 543288098430, 139081753198206, 35604928818740862, 9114861777597660798, 2333404615065001164414, 597351581456640298090110

Offset: 0

Abilene Sukin, Nov 28 2017

The n-th term of this sequence is the result of forming an ASCII (American Standard Code for Information Exchange) text string of n characters using the (printable) character with the largest binary value and then converting the binary value of the string to base 10. a(n) is therefore a measure of the largest possible size of an ASCII string with n printable characters. This sequence uses standard 7-bit ASCII; A175824 is the same sequence using 8-bit Extended ASCII.
Conjecture: For every a(n) there exists a sequence of primes (p(1), p(2), p(3), ...)  such that for each term a(n) there exists a set of primes that when added to the term result in another prime. For example, a(2)=126 and 126 + {5,11,13,23,37,41,47,...} all are primes.
Corollary 1: If it is the case that the size of the set of prime numbers is countably infinite, then the cardinality of the sequence that contains the sequence of primes p(1), p(2), ... that produce a new prime for every a(n) is uncountably infinite ... [ (a(1)+p(1), a(1)+p(2), a(1)+p(3), ...), (a(2)+p(1)', a(2)+p(2)', a(2)+p(3)'), ...)

			The lexicographically last 2-character printable ASCII string is "~~", which is 7E7E in hexadecimal or 32382 in decimal, thus a(2) = 32382.

Iain Fox, Table of n, a(n) for n = 0..415
Index entries for linear recurrences with constant coefficients, signature (257,-256).

Cf. A175824.

[(42/85)*(256^n - 1) : n in [0..20]]; // Wesley Ivan Hurt, Nov 29 2017

A295838:=n->(42/85)*(256^n - 1): seq(A295838(n), n=0..20); # Wesley Ivan Hurt, Nov 29 2017

Array[(42/85) (256^# - 1) &, 11, 0] (* Michael De Vlieger, Dec 11 2017 *)
CoefficientList[Series[126 x/((1 - 256 x) (1 - x)), {x, 0, 10}], x] (* Michael De Vlieger, Dec 11 2017 *)

a(n) = 42/85*(256^n-1) \\ Iain Fox, Nov 28 2017

first(n) = Vec(126*x/((1-256*x)*(1-x)) + O(x^n), -n) \\ Iain Fox, Nov 28 2017

a(n) = (42/85)*(256^n - 1).
From Iain Fox, Nov 28 2017: (Start)
G.f.: 126*x/((1-256*x)*(1-x)).
E.g.f.: 42/85*(e^(256*x)-e^x).
a(n) = 42/85 * A175824(n).
(End)
For n > 0, a(n) = 256*a(n-1) + 126. - Jon E. Schoenfield, Nov 29 2017
For n > 1, a(n) = 257*a(n-1) - 256*a(n-2). - Iain Fox, Jan 02 2018

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A175825 Maximum signed integer that can be stored in n bytes.

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A295838 Largest value corresponding to a string of n printable ASCII characters.

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