A065821 a(n) is the smallest prime ending in exactly n 1's.

31, 11, 2111, 101111, 311111, 29111111, 61111111, 1711111111, 14111111111, 31111111111, 311111111111, 2111111111111, 31111111111111, 3511111111111111, 5111111111111111, 101111111111111111, 3511111111111111111, 2111111111111111111, 1111111111111111111, 911111111111111111111

Offset: 1

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Nov 23 2001

Keywords

• base
• nonn

Examples

			a(4) = 101111 because 1111=11*101, 21111=3*31*227, 31111=53*587, 41111=7^2*829, 51111=3^4*631, 61111=23*2657, 71111=17*47*89, 81111=3*19*1423, 91111=179*509 so 101111 is the first prime ending in four 1's.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A037055, A065584, A065580, A065581, A065582.

Programs

Mathematica

pe[n_]:=Module[{k=0,len=IntegerLength[n]},While[Mod[k,10]==1||(!PrimeQ[ k*10^len+n]),k++];k*10^len+n]; pe/@Table[(10^n-1)/9,{n,20}] (* Harvey P. Dale, Dec 31 2013 *)_

PARI

a(n)={ my(f=10^n, b=(f-1)/9, k=0); while (!isprime(b + k*f), k+=1+(k%10==0)); b + k*f } \\ Harry J. Smith, Nov 01 2009

Extensions

Edited and extended by Robert G. Wilson v, Jul 04 2003