A104644 a(n) is the smallest prime divisor of the number obtained from concatenation of the first n primes.

2, 23, 5, 2357, 7, 23, 11, 7, 61, 3, 17, 7, 25391, 6899, 1597, 3, 17, 3, 1019, 3, 17, 211, 41378209, 3, 479, 3, 262343078386137703, 3, 107, 3, 643, 3, 7, 3, 13, 3, 107069, 7, 14733071537, 3, 61911427, 3, 13, 3, 31, 3, 11, 59, 7, 647, 31, 3, 13, 3, 31517, 43, 3, 19

Offset: 1

Author

Labos Elemer, Mar 18 2005

Keywords

• nonn
• base

Examples

			n=5, concatenation of {2,3,5,7,11} is 235711=7*151*223, smallest prime factor is a(5)=7.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..113
• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
• Hisanori Mishima, Smarandache consecutive prime sequences (n = 1 to 100).

Crossrefs

Cf. A019518, A020639, A074809.

Programs

Mathematica

Map[FactorInteger[FromDigits@ #][[1, 1]] &, Rest@ FoldList[Join @@ {#1, IntegerDigits[#2]} &, {}, Prime@ Range@ 29]] (* Michael De Vlieger, Jul 31 2017 *)

PARI

a(n) = vecmin(factor(eval(concat(concat([""], primes(n)))))[,1]); \\ Michel Marcus, Aug 01 2017

Formula

a(n) = A020639(A019518(n)). - Michel Marcus, Aug 01 2017

Extensions

a(29) and further terms from Robert G. Wilson v, Mar 18 2005

Edited by Charles R Greathouse IV, Apr 23 2010