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%I #7 Nov 24 2024 09:37:55
%S 1,1,2,3,4,5,6,7,8,9,10,3,6,12,7,14,10,20,6,18,20,40,12,24,19,25,22,
%T 14,28,29,30,12,36,30,60,25,50,20,60,120,15,30,90,40,80,38
%N a(1) = 1. For n > 1 if a(n-1) is a novel term a(n) = number of a(i); 1 <= i <= n-1 whose sum of decimal digits does not exceed A007953(a(n-1)). If a(n-1) has occurred k (>1) times, a(n) = k*a(n-1).
%C The first condition of the definition implies that if a(n-1) is a novel term then a(n) <= n-1, with equality iff A007953(a(n-1)) >= A007953(a(i)); i = 1,2,...n-1. Only the second condition of the definition can produce a(n) > n, consequent to repeats of a(n-1).
%e a(1) = 1 (given novel term) means a(2) = 1 since there is just one term having digit sum not exceeding 1. Since 1 has now occurred twice, a(3) = 2*1 = 2, another novel term with digit sum = 2. Since there are now 3 terms up to and including a(3) = 3 with digit sum at most 3, a(4) = 3. This pattern continues(4,5,6..) until reaching a(11) = 10, a novel term with digit sum = 1. At this point the number of terms in a(1),a(2),...a(11) having digit sum equal to at most 1 is 3, so a(12) = 3. Then since 3 has been seen twice, a(13) = 6; and so on.
%Y Cf. A007953.
%K nonn,base,more,new
%O 1,3
%A _David James Sycamore_, Nov 22 2024