A034388 -id:A034388 - cp's OEIS frontend

A084673 Smallest prime in which a digit appears n times.

2, 11, 1117, 10111, 101111, 1111151, 11110111, 101111111, 1111111121, 11111111113, 101111111111, 1111111118111, 11111111111411, 111111111116111, 1111111111111181, 11111111101111111, 101111111111111111

Offset: 1

Harvey P. Dale, Jun 29 2003

For n > 1, conjectured to be equal to A037055(n), the smallest prime in { R-10^n, R-10^(n-1), ..., R-10; R+a*10^b, a = 1, ..., 8, b = 0, 1, 2, ..., n }, where R = (10^(n+1)-1)/9 is the (n+1)-digit repunit. - M. F. Hasler, Feb 25 2016

			a(4)=10111 because 10111 is the smallest prime with four duplicate digits.

Liz Strachan, Numbers are Forever, Mathematical Facts and Curiosities, Constable, London, 2014, page 267.

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Cf. A034388, A037055, A065584, A065821.

Table[ First[ Select[ Prime[ Range[100000]], Max[ DigitCount[ # ]]==i & ]], {i, 6}] (* or *)
f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[ b, {i, 1, n}], {x}]], c = Complement[ Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[ r != Infinity, r, While[ !PrimeQ[k] || Count[ IntegerDigits[k], b] != n, k++ ]; k]]; Table[ f[n, 1], {n, 2, 18}]

A084673(n)=if(n>1,A037055(n),2) \\ M. F. Hasler, Feb 25 2016

Edited and extended by Robert G. Wilson v, Jul 03 2003

A131316 Smallest prime beginning with exactly n identical digits.

Original entry on oeis.org

2, 11, 1117, 11113, 111119, 3333331, 11111117, 111111113, 4444444447, 11111111113, 444444444443, 5555555555551, 22222222222229, 222222222222227, 11111111111111101, 11111111111111119, 222222222222222221, 8888888888888888881, 1111111111111111111

Offset: 1

Shyam Sunder Gupta, Sep 29 2007

			a(4) = 11113 because 11113 is the smallest prime beginning with exactly 4 identical digits.
a(18) = 8888888888888888881 > a(19) = 1111111111111111111, which begins with exactly 19 identical digits. - _Alois P. Heinz_, Sep 05 2011

Alois P. Heinz, Table of n, a(n) for n = 1..200

Different from A034388.

More terms from Alois P. Heinz, Sep 05 2011

cp's OEIS Frontend

A084673 Smallest prime in which a digit appears n times.

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