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

1,3

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.

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A007953, A378293, A378782, A356348.

Sequence in context: A327529 A318775 A317500 * A339420 A317494 A317505

Adjacent sequences: A378849 A378850 A378851 * A378853 A378854 A378856

Keyword

nonn,base,look,changed

Author

David James Sycamore, Dec 09 2024

Extensions

More terms from David A. Corneth, Dec 24 2024

Status

approved