A096499 - OEIS

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A096499

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

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

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..61.

FORMULA

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

EXAMPLE

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

MATHEMATICA

<<NumberTheory`NumberTheoryFunctions` Table[NextPrime[(10^n-1)/9]-PreviousPrime[(10^n-1)/9], {n, 2, 100}]

dpf[n_]:=Module[{ru=FromDigits[PadRight[{}, n, 1]]}, NextPrime[ru]-NextPrime[ ru, -1]]; Array[dpf, 60, 2] (* Harvey P. Dale, Sep 06 2015 *)