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A330291 a(1) = 1; for n > 1, a(n) is the smallest prime divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.

%I A330291 #14 Jan 08 2025 09:27:24
%S A330291 1,1,11,101,3,17,65358901,7,109,10193590070216413001,359,4007,149,
%T A330291 43787,169031777,67,13,14767,30323,151651,1194421,
%U A330291 31008087256045370298219860945197217288544368471059741857398977350440454626775436666667,1087,27457,19301,23,22349
%N A330291 a(1) = 1; for n > 1, a(n) is the smallest prime divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.
%C A330291 The next term a(28) requires the factorization of a composite 195 digit number 49715...700001. Note that for the second term 1 is considered to be prime.
%H A330291 Tyler Busby, <a href="/A330291/b330291.txt">Table of n, a(n) for n = 1..57</a>
%e A330291 a(3) = 11 as the concatenation of a(1) and a(2) = '11' and 11, the smallest prime divisor of 11, has not appeared in the sequence.
%e A330291 a(4) = 101 as the concatenation of a(1)..a(3) is '1111' and 101 is the smallest prime divisor of 1111 which has not appeared in the sequence. Note that 11 also divides 1111 but a(3) = 11.
%e A330291 a(6) = 17 as the concatenation of a(1)..a(5) is '11111013' and 17 is the smallest prime divisor of 11111013 which has not appeared in the sequence. Note that 9 also divides 11111013 and has not appeared but only prime divisors are considered.
%Y A330291 Cf. A000040, A020639, A240588, A330290, A330293.
%K A330291 nonn,base
%O A330291 1,3
%A A330291 _Scott R. Shannon_, Dec 09 2019