A096869 -id:A096869 - cp's OEIS frontend

A096497 Prime following n-th repunit.

2, 13, 113, 1117, 11113, 111119, 1111151, 11111117, 111111113, 1111111121, 11111111113, 111111111149, 1111111111139, 11111111111123, 111111111111229, 1111111111111123, 11111111111111119, 111111111111111131, 1111111111111111171, 11111111111111111131, 111111111111111111157, 1111111111111111111189

Offset: 1

Labos Elemer, Jul 09 2004

nonn

Not equal to A068693: first and 2nd terms differ.

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A068693, A002275.

Table[NextPrime[(10^n-1)/9], {n, 40}]
Table[NextPrime[FromDigits[PadRight[{},n,1]]],{n,30}] (* Harvey P. Dale, Aug 11 2023 *)

a(n) = nextprime((10^n-1)/9 + 1); \\ Michel Marcus, May 02 2016

from sympy import nextprime
def A096497(n):
    return nextprime((10**n-1)//9) # Chai Wah Wu, Nov 04 2019

a(n) = A002275(n) + A096869(n) = A096498(n) + A096499(n).

A096499 Difference between prime following and prime preceding n-th repunit.

Original entry on oeis.org

6, 4, 8, 20, 10, 60, 16, 4, 24, 54, 46, 46, 70, 176, 84, 12, 40, 134, 104, 104, 92, 24, 84, 270, 300, 130, 414, 90, 88, 240, 148, 198, 12, 64, 12, 300, 66, 70, 80, 102, 420, 142, 630, 140, 600, 88, 176, 312, 80, 96, 460, 132, 420, 284, 144, 408, 312, 180, 44, 300

Offset: 2

Labos Elemer, Jul 09 2004

nonn

			n=2: 2nd repunit=11, 13-7=6=a[2].

Cf. A068693, A002275, A096497, A096498.

Mathematica
```
<Harvey P. Dale, Sep 06 2015 *)
```

a(n) = A096497(n) - A096498(n) = A096869(n) + A096870(n).

A096870 Difference between the n-th repunit and the previous prime.

Original entry on oeis.org

4, 2, 2, 18, 2, 20, 10, 2, 14, 52, 8, 18, 58, 58, 72, 4, 20, 74, 84, 58, 14, 18, 82, 168, 28, 50, 168, 84, 8, 138, 112, 82, 2, 28, 2, 62, 34, 50, 74, 24, 8, 54, 204, 22, 428, 40, 118, 200, 72, 40, 30, 42, 284, 44, 114, 268, 80, 18, 4, 74, 142, 182, 140, 112, 214, 152, 90

Offset: 2

Robert G. Wilson v, Jul 12 2004

nonn

Robert Israel, Table of n, a(n) for n = 2..1000

Cf. A096869.

f:= proc(n) local r; r:= (10^n-1)/9; r - prevprime(r) end proc:
map(f, [$2..100]); # Robert Israel, Feb 23 2017

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Table[(10^n - 1)/9 - PrevPrim[(10^n - 1)/9], {n, 2, 70}]
Table[With[{ru=(10^n-1)/9},ru-NextPrime[ru,-1]],{n,2,70}] (* Harvey P. Dale, Aug 14 2011 *)

a(n) = A002275(n) - A096498(n) = A096499(n) - A096869(n).

cp's OEIS Frontend

A096497 Prime following n-th repunit.

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A096499 Difference between prime following and prime preceding n-th repunit.

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A096870 Difference between the n-th repunit and the previous prime.

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