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

Author

Harvey P. Dale, Jun 29 2003

Keywords

• nonn
• base

Comments

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

Examples

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

References

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

Links

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

Crossrefs

Cf. A034388, A037055, A065584, A065821.

Programs

Mathematica

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}]

PARI

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

Extensions

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