A065075 -id:A065075 - cp's OEIS frontend

A139417 Sum of digits of the square of the sum of the preceding numbers.

1, 1, 4, 9, 9, 18, 18, 9, 18, 27, 27, 27, 18, 27, 27, 18, 27, 18, 27, 18, 9, 27, 27, 27, 27, 18, 27, 9, 27, 27, 27, 9, 27, 27, 36, 27, 27, 27, 18, 27, 27, 27, 27, 27, 36, 36, 9, 27, 27, 18, 36, 36, 27, 18, 27, 18, 27, 27, 27, 27, 36, 36, 27, 18, 36, 27, 36

Offset: 1

Philippe Lallouet (philip.lallouet(AT)orange.fr), Apr 20 2008

As soon as a term is 9 or multiple of 9, which is true for a(4), all following ones are also multiple of 9, which never occurs in A065075.

Cf. A065075.

nxt[{t_,a_}]:=Module[{c=Total[IntegerDigits[t^2]]},{t+c,c}]; NestList[ nxt,{1,1},70][[All,2]] (* Harvey P. Dale, Jun 15 2021 *)

def sd(n): return sum(map(int, str(n)))
def aupton(terms):
    alst, s = [1], 1
    for n in range(2, terms+1): alst.append(sd(s**2)); s += alst[-1]
    return alst
print(aupton(67)) # Michael S. Branicky, Jun 15 2021

Corrected and extended by Harvey P. Dale, Jun 15 2021

A162251 Sum of digits of product of previous terms, with a(1) = 2.

Original entry on oeis.org

2, 2, 4, 7, 4, 16, 22, 34, 31, 34, 49, 70, 67, 61, 85, 88, 76, 70, 94, 106, 76, 133, 139, 133, 157, 187, 193, 187, 202, 196, 220, 196, 202, 214, 229, 232, 301, 259, 247, 304, 346, 304, 337, 358, 355, 358, 328, 376, 409, 412, 445, 466, 472, 466, 445, 475, 481, 520

Offset: 1

Franklin T. Adams-Watters, Jun 28 2009

Starting with a(1) = 1 produces the all 1's sequence.

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

Cf. A065075, A048572, A000012.

A[1]:= 2: P:= 2:
for n from 2 to 100 do
  x:= convert(convert(P,base,10),`+`);
  if length(x) > 997 then break fi;
  A[n]:= x;
  P:= P*x;
od:
seq(A[i],i=1..100); # Robert Israel, Jan 16 2025

A169734 a(1) = 1000; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).

Original entry on oeis.org

1000, 1001, 1003, 1007, 1015, 1022, 1027, 1037, 1048, 1061, 1069, 1085, 1099, 1118, 1129, 1142, 1150, 1157, 1171, 1181, 1192, 1205, 1213, 1220, 1225, 1235, 1246, 1259, 1276, 1292, 1306, 1316, 1327, 1340, 1348, 1364, 1378, 1397, 1417, 1430, 1438, 1454

Offset: 1

N. J. A. Sloane, May 01 2010

First differences are A065075. Cf. A169732.

f:=proc(n) global S; option remember; if n=1 then RETURN(S) else RETURN(f(n-1)+digsum(f(n-1))); fi; end; S:=1000; [seq(f(n),n=1..120)];

A240919 Sequence whose n-th term is the sum of the first n digits in the concatenation of the base 10-representation of the sequence.

Original entry on oeis.org

9, 10, 10, 11, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 27, 28, 33, 34, 40, 41, 49, 50, 59, 61, 63, 65, 68, 70, 77, 79, 87, 90, 93, 96, 100, 104, 104, 108, 109, 113, 122, 127, 127, 132, 141, 147, 148, 154, 157, 163

Offset: 1

Anthony Zajac, Aug 02 2014

This is the unique sequence in base 10 with this property, aside from the trivial case of beginning this sequence with a(k)=0 for the first k terms.
The only possible nonzero values for a(1) and a(2) are 9 and 10, respectively. This is because a(1) must be a 1-digit number, while a(2) must equal the sum of its own first digit and a(1).
Likewise, for the analogous sequence in a different base b, the first two terms must be b-1 and b.
Essentially the same as A107975. - R. J. Mathar, Jul 07 2023

			a(5) is the sum of the first 5 digits of "91010111112..." = 9 + 1 + 0 + 1 + 0 = 11.

Anthony Zajac, Table of n, a(n) for n = 1..10000

Cf. A004207, A016096, A061939, A065075, A107975.

a240919 = {};
Do[
Which[Length[a240919] <= 0, AppendTo[a240919, 9],
  Length[a240919] == 1,
  AppendTo[a240919,
   First[First[a240919] +
     IntegerDigits[First[Plus[a240919, a240919]]]]],
  True, AppendTo[a240919,
   Total[Take[Flatten[Map[IntegerDigits, a240919]], n]]]], {n,
  10000}]; TableForm[
Transpose[
  List[Range[Length[a240919]],
   a240919]]] (* Michael De Vlieger, Aug 05 2014 *)

lista(nn) = {v = vector(nn); v[1] = 9; v[2] = 10; vd = [9, 1, 0]; print1(v[1], ", ", v[2], ", "); for (n=3, nn, v[n] = sum(k=1, n, vd[k]); vd = concat(vd, digits(v[n])); print1(v[n], ", "););} \\ Michel Marcus, Aug 14 2014

A112436 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 10, 11, 13, 17, 25, 22, 25, 30, 29, 32, 30, 29, 33, 36, 34, 36, 42, 37, 41, 37, 40, 35, 37, 37, 42, 38, 45, 46, 46, 46, 50, 44, 43, 40, 34, 31, 30, 25, 25, 28, 31, 31, 32, 30, 26, 24, 26, 30, 28, 35, 35, 37, 39, 48, 50, 47, 50, 45, 42, 36, 40, 33

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(28)=42 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(28)=42 because 2+9 + 3+3 + 3+6 + 3+4 + 3+6 = 42

Cf. A112395, A004207, A065075, A001370.

A112438 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 14, 19, 29, 40, 44, 38, 44, 42, 37, 43, 42, 37, 39, 45, 44, 45, 48, 50, 43, 41, 38, 40, 32, 32, 30, 28, 27, 32, 32, 32, 34, 31, 26, 29, 35, 38, 42, 44, 44, 41, 38, 38, 43, 42, 40, 39, 40, 33, 32, 31, 31, 23, 24, 24, 25, 28, 34, 36, 39, 45, 47, 48

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(18)=44 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(18)=44 because 1+9 + 2+9 + 4+0 + 4+4 + 3+8 = 44

Cf. A112395, A004207, A065075, A001370.

A112439 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 16, 23, 28, 38, 49, 46, 49, 57, 59, 62, 57, 59, 60, 54, 49, 54, 51, 43, 44, 43, 37, 38, 43, 43, 42, 41, 36, 34, 34, 34, 35, 38, 40, 37, 40, 37, 39, 40, 40, 34, 37, 37, 35, 39, 47, 51, 47, 48, 52, 47, 47, 52, 48, 48, 53, 50, 44, 45, 42, 36, 37, 42

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(32)=37 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(32)=37 because 5+4 + 5+1 + 4+3 + 4+4 + 4+3 = 37

Cf. A112395, A004207, A065075, A001370.

A112440 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 18, 27, 36, 45, 54, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(17)=45 and the loop has one term. Computed by Gilles Sadowski.

			a(17)=45 because 1+8 + 2+7 + 3+6 + 4+5 + 5+4 = 45

Cf. A112395, A004207, A065075, A001370.

A169737 a(1) = 100; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).

Original entry on oeis.org

100, 101, 103, 107, 115, 122, 127, 137, 148, 161, 169, 185, 199, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538, 554, 568, 587, 607, 620, 628, 644, 658, 677, 697, 719, 736, 752

Offset: 1

N. J. A. Sloane, May 01 2010

Cf. A169732, A007618. First differences are A065075.

NestList[#+Total[IntegerDigits[#]]&,100,60] (* Harvey P. Dale, Aug 23 2019 *)

cp's OEIS Frontend

A139417 Sum of digits of the square of the sum of the preceding numbers.

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A162251 Sum of digits of product of previous terms, with a(1) = 2.

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A169734 a(1) = 1000; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).

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A240919 Sequence whose n-th term is the sum of the first n digits in the concatenation of the base 10-representation of the sequence.

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PARI

A112436 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 5.

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A112438 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 7.

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A112439 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 8.

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A112440 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.

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A169737 a(1) = 100; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).

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