A105436 Smallest prime that remains prime when a string of n 1's is appended to it.

2, 3, 2, 2, 13, 3, 29, 7, 17, 17, 3, 3, 2, 3, 197, 5, 13, 173, 2, 13, 53, 73, 199, 2, 23, 73, 599, 239, 547, 59, 409, 1009, 1277, 19, 3, 383, 137, 13, 653, 103, 139, 227, 19, 127, 359, 193, 1123, 3, 97, 1447, 839, 109, 3, 47, 17, 7, 269, 2, 1657, 1973, 709, 5233, 809

Offset: 0

Author

Lekraj Beedassy, Apr 08 2005

Keywords

• nonn
• base

Examples

			a(2)=2 because it is the first prime followed by 3,41,101,107,113,137,... all remaining primes when 11 is appended to each of them.
		

Crossrefs

Cf. A065821, A105437.

Programs

Maple

with(numtheory); for n from 1 to 100 do for i from 1 to 5000 do if isprime(ithprime(i)*10^n + sum(10^j, j=0..n-1)) then printf(`%d,`, ithprime(i)); break; fi: od:od: # James Sellers, Apr 09 2005

Mathematica

f[n_] := Block[{k = 1, t = Table[1, {n}]}, While[id = IntegerDigits[ Prime[k]]; id[[ -1]] == 1 || !PrimeQ[ FromDigits[ Join[id, t]]], k++ ]; Prime[k]]; Table[ f[n], {n, 0, 62}] (* Robert G. Wilson v, Apr 09 2005 *)

Extensions

More terms from Robert G. Wilson v and James Sellers, Apr 09 2005