A072921 a(1)=1; a(n) = a(n-1) + [sum of all decimal digits present so far in the sequence].

1, 2, 5, 13, 25, 44, 71, 106, 148, 203, 263, 334, 415, 506, 608, 724, 853, 998, 1169, 1357, 1561, 1778, 2018, 2269, 2539, 2828, 3137, 3460, 3796, 4157, 4535, 4930, 5341, 5765, 6212, 6670, 7147, 7643, 8159, 8698, 9268, 9863, 10484, 11122

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(1)=1, a(2)=2; a(n+1)=2a(n)-a(n-1)+sod(a(n)) (sod = "sum of digits"). - Farideh Firoozbakht, Oct 01 2009

Asymptotically it seems a(n)~c*n^2*log(n) for c~1.99... - Benoit Cloitre, Oct 07 2009

Maple

b:= proc(n) option remember; local m;
      m:= a(n);
      `if`(n=1, 0, b(n-1));
       while m>0 do %+ irem(m, 10, 'm') od; %
    end:
a:= proc(n) option remember;
      `if`(n=1, 1, a(n-1) +b(n-1))
    end:
seq(a(n), n=1..50); # Alois P. Heinz, Jun 01 2010

Mathematica

a[1]=1; a[2]=2; a[n_]:=a[n]=2*a[n-1]-a[n-2]+Apply[Plus, IntegerDigits[a[n-1]]]; Table[a[n], {n, 100}] (* Farideh Firoozbakht, Oct 01 2009 *)
a[1] = 1; a[n_] := a[n] = a[n - 1] + Plus @@ Flatten[ Map[ IntegerDigits, Array[a, n - 1]]]; Array[a, 100] (* Robert G. Wilson v, Oct 01 2009 *)

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, anp1 = 1, 2
    while True:
        yield an
        an, anp1 = anp1, 2*anp1 - an + sum(map(int, str(anp1)))
print(list(islice(agen(), 44))) # Michael S. Branicky, Oct 01 2024

Crossrefs

Cf. A007953, A152231, A152232, A152233, A152234.

Sequence in context: A309230 A048871 A324702 * A369714 A289529 A087250

Adjacent sequences: A072918 A072919 A072920 * A072922 A072923 A072924

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 07 2009, based on a posting to the Sequence Fans Mailing List by Eric Angelini, Oct 01 2009

Extensions

More terms from Alois P. Heinz, Oct 01 2009

Status

approved