A378852 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.

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, 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, 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

Offset: 1

Author

David James Sycamore, Dec 09 2024

Keywords

• nonn
• base
• look

Comments

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.

Compare with A356348 and A378782.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A378293, A378782, A356348.

Programs

Maple

R:= 1: dR:= 1:
for n from 2 to 100 do
  v:= nops(select(i -> dR[i] >= dR[n-1], [$1..n-1]));
  R:= R,v; dR:= dR, convert(convert(v,base,10),`+`);
od:
R; # Robert Israel, Feb 09 2025

PARI

first(n) = {
	my(res = vector(n), digs = vector(n));
	res[1] = 1; digs[1] = 1;
	for(i = 2, n,
		s = 1 + sum(j = 1, i-2, digs[j] >= digs[i-1]);
		res[i] = s;
		digs[i] = sumdigits(s)
	);
	res
} \\ David A. Corneth, Dec 24 2024

Extensions

More terms from David A. Corneth, Dec 24 2024