|
%I #4 Mar 30 2012 18:40:43
%S 2,21,213,2134,21347,2134711,213471118,21347111829,2134711182947,
%T 213471118294776,213471118294776123,213471118294776123199,
%U 213471118294776123199322,213471118294776123199322521
%N Cumulative concatenation of A000032 Lucas numbers (beginning at 2).
%C 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.
%F a(1) = 2; a(n+1) = Concatenate(a(n),A000032(n+1)).
%e Table of first 14 values, with factorizations:
%e n a(n) factors
%e 1 2 prime
%e 2 21 3 * 7 semiprime
%e 3 213 3 * 71 semiprime
%e 4 2134 2 * 11 * 97
%e 5 21347 is prime
%e 6 2134711 719 * 2969 semiprime
%e 7 213471118 = 2 * 7 * 19 * 802523
%e 8 21347111829 = 3 * 12743 * 558401
%e 9 2134711182947 = 7 * 491 * 621097231
%e 10 213471118294776 = 2^3 * 3^2 * 41 * 7349 * 9839987
%e 11 213471118294776123 = 3 * 41 * 785903 * 2208335567
%e 12 213471118294776123199 = 11 * 23 * 349 * 2417648598420967
%e 13 213471118294776123199322 = 2 * 23 * 37 * 3929 * 6991 * 4566234789049
%e 14 213471118294776123199322521 = 61950375139 * 3445840607353939 semiprime.
%Y Cf. A000032, A000204, A130774.
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 15 2007
| 