A378852 - OEIS

%I #15 Dec 26 2024 20:07:36

%S 1,1,2,1,4,1,6,1,8,1,10,11,5,3,5,4,6,3,9,1,20,13,9,2,16,4,12,15,7,5,

%T 11,23,12,20,26,4,18,3,24,11,32,16,8,6,14,20,38,1,48,1,50,23,24,17,9,

%U 6,20,47,3,40,35,12,43,16,17,13,40,41,34,19,4,45,9,10,74,4,49,1,78,1,80

%N a(1) = 1. For n > 1 a(n) is the number of terms a(i); 1 <= i <= n-1 such that d(a(i)) >= d(a(n-1)), where d is the decimal digital sum function A007953.

%C d(a(n-1)) >= d(a(i)); 1 <= i <= n-1 implies a(n) = 1. a(n) <= n-1 for all n > 1, with equality iff d(a(n-1)) = 1.

%C Compare with A356348 and A378782.

%e a(1) = 1 so a(2) also = 1 since there is only one term up to and including a(1) = 1 which has digit sum >= 1. Then a(3) = 2 because now there are two terms having digit sum >= 1. a(11) = 10 so a(12) = 11 since all terms up to and including a(11) have digit sum >= 1. a(19) = 9, whose digit sum (9) sets a record, thus a(20) = 1, which means a(21) = 20.

%o (PARI) first(n) = {

%o 	my(res = vector(n), digs = vector(n));

%o 	res[1] = 1; digs[1] = 1;

%o 	for(i = 2, n,

%o 		s = 1 + sum(j = 1, i-2, digs[j] >= digs[i-1]);

%o 		res[i] = s;

%o 		digs[i] = sumdigits(s)

%o 	);

%o 	res

%o } \\ _David A. Corneth_, Dec 24 2024

%Y Cf. A007953, A378293, A378782, A356348.

%K nonn,base,new

%O 1,3

%A _David James Sycamore_, Dec 09 2024

%E More terms from _David A. Corneth_, Dec 24 2024