A131698 Cumulative concatenation of A000032 Lucas numbers (beginning at 2).

2, 21, 213, 2134, 21347, 2134711, 213471118, 21347111829, 2134711182947, 213471118294776, 213471118294776123, 213471118294776123199, 213471118294776123199322, 213471118294776123199322521

Offset: 1

Author

Jonathan Vos Post, Sep 15 2007

Keywords

• base
• easy
• nonn

Comments

This is to A000032 as A130774 is to A000204. Like these Lucas numbers, a(n) cycles even, odd, odd, even, odd, odd, ... a(n) is prime for n = 1, 5 and semiprime for n = 2, 3, 6, 14. No more prime nor semiprime values through n = 60, which has a 381 digit composite factor.

Examples

			Table of first 14 values, with factorizations:
n a(n) factors
1 2 prime
2 21 3 * 7 semiprime
3 213 3 * 71 semiprime
4 2134 2 * 11 * 97
5 21347 is prime
6 2134711 719 * 2969 semiprime
7 213471118 = 2 * 7 * 19 * 802523
8 21347111829 = 3 * 12743 * 558401
9 2134711182947 = 7 * 491 * 621097231
10 213471118294776 = 2^3 * 3^2 * 41 * 7349 * 9839987
11 213471118294776123 = 3 * 41 * 785903 * 2208335567
12 213471118294776123199 = 11 * 23 * 349 * 2417648598420967
13 213471118294776123199322 = 2 * 23 * 37 * 3929 * 6991 * 4566234789049
14 213471118294776123199322521 = 61950375139 * 3445840607353939 semiprime.
		

Crossrefs

Cf. A000032, A000204, A130774.

Formula

a(1) = 2; a(n+1) = Concatenate(a(n),A000032(n+1)).