A345681 a(0) = 0; for n >= 1, a(n) = A004185(a(n-1)+n).

0, 1, 3, 6, 1, 6, 12, 19, 27, 36, 46, 57, 69, 28, 24, 39, 55, 27, 45, 46, 66, 78, 1, 24, 48, 37, 36, 36, 46, 57, 78, 19, 15, 48, 28, 36, 27, 46, 48, 78, 118, 159, 12, 55, 99, 144, 19, 66, 114, 136, 168, 129, 118, 117, 117, 127, 138, 159, 127, 168

Offset: 0

Author

Ctibor O. Zizka, Jun 22 2021

Keywords

• nonn
• base

Examples

			a(4) = A004185(6+4) = 1; a(13) = A004185(69+13) = 28.
		

Links

• Robert P. P. McKone, Table of n, a(n) for n = 0..2999

Crossrefs

Cf. A004185, A004719,

Programs

Mathematica

a[0] := 0;
a[n_] := FromDigits[Sort[DeleteCases[IntegerDigits[a[n - 1] + n], 0]]];
Table[a[n], {n, 0, 59}] (* Robert P. P. McKone, Aug 16 2021 *)

PARI

f(n) = fromdigits(vecsort(digits(n))); \\ A004185
a(n) = if (n==0, 0, f(a(n-1)+n)); \\ Michel Marcus, Jun 26 2021

PARI

f(n) = fromdigits(vecsort(digits(n))); \\ A004185
lista(nn) = {my(v=vector(nn)); v[1] = 1; for (n=2, nn, v[n] = f(v[n-1]+n);); concat(0, v);} \\ Michel Marcus, Jun 26 2021

Python

def A004185(n): return int("".join(sorted(str(n))).strip('0'))
def aupton(nn):
    alst = [0]
    for n in range(1, nn+1): alst.append(A004185(alst[-1]+n))
    return alst
print(aupton(100)) # Michael S. Branicky, Jun 22 2021

Formula

a(9*k+0 or 8) == 0 (mod 9);

a(9*k+1 or 4 or 7) == 1 (mod 9);

a(9*k+2 or 6) == 3 (mod 9);

a(9*k+3 or 5) == 6 (mod 9).