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

1,1

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.

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

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.

Sequence in context: A008351 A037743 A037638 * A163068 A109684 A292134

Adjacent sequences: A131695 A131696 A131697 * A131699 A131700 A131701

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Sep 15 2007

Status

approved