A072921 - OEIS

%I #21 Oct 01 2024 15:45:54

%S 1,2,5,13,25,44,71,106,148,203,263,334,415,506,608,724,853,998,1169,

%T 1357,1561,1778,2018,2269,2539,2828,3137,3460,3796,4157,4535,4930,

%U 5341,5765,6212,6670,7147,7643,8159,8698,9268,9863,10484,11122

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

%H Alois P. Heinz, <a href="/A072921/b072921.txt">Table of n, a(n) for n = 1..1000</a>

%F 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

%F Asymptotically it seems a(n)~c*n^2*log(n) for c~1.99... - _Benoit Cloitre_, Oct 07 2009

%p b:= proc(n) option remember; local m;

%p       m:= a(n);

%p       `if`(n=1, 0, b(n-1));

%p        while m>0 do %+ irem(m, 10, 'm') od; %

%p     end:

%p a:= proc(n) option remember;

%p       `if`(n=1, 1, a(n-1) +b(n-1))

%p     end:

%p seq(a(n), n=1..50); # _Alois P. Heinz_, Jun 01 2010

%t 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 *)

%t 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 *)

%o (Python)

%o from itertools import islice

%o def agen(): # generator of terms

%o     an, anp1 = 1, 2

%o     while True:

%o         yield an

%o         an, anp1 = anp1, 2*anp1 - an + sum(map(int, str(anp1)))

%o print(list(islice(agen(), 44))) # _Michael S. Branicky_, Oct 01 2024

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

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Oct 07 2009, based on a posting to the Sequence Fans Mailing List by _Eric Angelini_, Oct 01 2009

%E More terms from _Alois P. Heinz_, Oct 01 2009