A007612 -id:A007612 - cp's OEIS frontend

A004207 a(0) = 1, a(n) = sum of digits of all previous terms.

1, 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 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

Offset: 0

N. J. A. Sloane

If the leading 1 is omitted, this is the important sequence b(1)=1, for n >= 2, b(n) = b(n-1) + sum of digits of b(n-1). Cf. A016052, A016096, etc. - N. J. A. Sloane, Dec 01 2013
Same digital roots as A065075 (Sum of digits of the sum of the preceding numbers) and A001370 (Sum of digits of 2^n); they end in the cycle {1 2 4 8 7 5}. - Alexandre Wajnberg, Dec 11 2005
More precisely, mod 9 this sequence is 1 (1 2 4 8 7 5)*, the parenthesized part being repeated indefinitely. This shows that this sequence is disjoint from A016052. - N. J. A. Sloane, Oct 15 2013
There are infinitely many even terms (Belov 2003).
a(n) = A007618(n-5) for n > 57; a(n) = A006507(n-4) for n > 15. - Reinhard Zumkeller, Oct 14 2013

N. Agronomof, Problem 4421, L'Intermédiaire des mathématiciens, v. 21 (1914), p. 147.
D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 65.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. E. Stevens and L. G. Hunsberger, A Result and a Conjecture on Digit Sum Sequences, J. Recreational Math. 27, no. 4 (1995), pp. 285-288.
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 37.

T. D. Noe, Table of n, a(n) for n = 0..10000
A. Ya. Belov (ed.), Collection of monster problems in mathematics (in Russian), 2003. Problem 39.
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
J. Laroche & N. J. A. Sloane, Correspondence, 1977
Project Euler, Problem 551: Sum of digits sequence.
Kenneth B. Stolarsky, The sum of a digitaddition series, Proc. Amer. Math. Soc. 59 (1976), no. 1, 1--5. MR0409340 (53 #13099)
Index entries for Colombian or self numbers and related sequences

Cf. A016052, A016096, A033298, A007612, A007953, A229527, A230107.
For the base-2 analog see A010062.
A065075 gives sum of digits of a(n).
See A219675 for an essentially identical sequence.

a004207 n = a004207_list !! n
a004207_list = 1 : iterate a062028 1
-- Reinhard Zumkeller, Oct 14 2013, Sep 12 2011

read("transforms") :
A004207 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        add( digsum(procname(i)),i=0..n-1) ;
    end if;
end proc: # R. J. Mathar, Apr 02 2014
# second Maple program:
a:= proc(n) option remember; `if`(n<2, 1, (t->
     t+add(i, i=convert(t, base, 10)))(a(n-1)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Jul 31 2022

f[s_] := Append[s, Plus @@ Flatten[IntegerDigits /@ s]]; Nest[f, {1}, 55] (* Robert G. Wilson v, May 26 2006 *)
f[n_] := n + Plus @@ IntegerDigits@n; Join[{1}, NestList[f, 1, 80]] (* Alonso del Arte, May 27 2006 *)

a(n) = { my(f(d, i) = d+vecsum(digits(d)), S=vector(n)); S[1]=1; for(k=1, n-1, S[k+1] = fold(f, S[1..k])); S } \\ Satish Bysany, Mar 03 2017

a = 1; print1(a, ", "); for(i = 1, 50, print1(a, ", "); a = a + sumdigits(a)); \\ Nile Nepenthe Wynar, Feb 10 2018

from itertools import islice
def agen():
    yield 1; an = 1
    while True: yield an; an += sum(map(int, str(an)))
print(list(islice(agen(), 54))) # Michael S. Branicky, Jul 31 2022

For n>1, a(n) = a(n-1) + sum of digits of a(n-1).

For n > 1: a(n) = A062028(a(n-1)). - Reinhard Zumkeller, Oct 14 2013

Errors from 25th term on corrected by Leonid Broukhis, Mar 15 1996

Typo in definition fixed by Reinhard Zumkeller, Sep 14 2011

A047235 Numbers that are congruent to {2, 4} mod 6.

Original entry on oeis.org

2, 4, 8, 10, 14, 16, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 92, 94, 98, 100, 104, 106, 110, 112, 116, 118, 122, 124, 128, 130, 134, 136, 140, 142, 146, 148, 152, 154, 158, 160, 164, 166, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 206

Offset: 1

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 19 ).
Complement of A047273; A093719(a(n)) = 0. - Reinhard Zumkeller, Oct 01 2008
One could prefix an initial term "1" (or not) and define this sequence through a(n+1) = a(n) + (a(n) mod 6). See A001651 for the analog with 3, A235700 (with 5), A047350 (with 7), A007612 (with 9) and A102039 (with 10). Using 4 or 8 yields a constant sequence from that term on. - M. F. Hasler, Jan 14 2014
Nonnegative m such that m^2/6 + 1/3 is an integer. - Bruno Berselli, Apr 13 2017
Numbers divisible by 2 but not by 3. - David James Sycamore, Apr 04 2018
Numbers k for which A276086(k) is of the form 6m+3. - Antti Karttunen, Dec 03 2022

David A. Corneth, Table of n, a(n) for n = 1..10000
Chunhui Lai, A note on potentially K_4-e graphical sequences, arXiv:math/0308105 [math.CO], 2003.
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A020760, A020832, A093719, A047273 (complement), A120325 (characteristic function).
Equals 2*A001651.
Cf. A007310 ((6*n+(-1)^n-3)/2). - Bruno Berselli, Jun 24 2010
Positions of 3's in A053669 and in A358840.

[ n eq 1 select 2 else Self(n-1)+2*(1+n mod 2): n in [1..70] ]; // Klaus Brockhaus, Dec 13 2008

seq(6*floor((n+1)/2) + 3 + (-1)^n, n=1..67); # Gary Detlefs, Mar 02 2010

Flatten[Table[{6n - 4, 6n - 2}, {n, 40}]] (* Alonso del Arte, Oct 27 2014 *)

a(n)=(n-1)\2*6+3+(-1)^n \\ Charles R Greathouse IV, Jul 01 2013

first(n) = my(v = vector(n, i, 3*i - 1)); forstep(i = 2, n, 2, v[i]--); v \\ David A. Corneth, Oct 20 2017

a(n) = 2*A001651(n).
n such that phi(3*n) = phi(2*n). - Benoit Cloitre, Aug 06 2003
G.f.: 2*x*(1 + x + x^2)/((1 + x)*(1 - x)^2). a(n) = 3*n - 3/2 - (-1)^n/2. - R. J. Mathar, Nov 22 2008
a(n) = 3*n + 5..n odd, 3*n + 4..n even a(n) = 6*floor((n+1)/2) + 3 + (-1)^n. - Gary Detlefs, Mar 02 2010
a(n) = 6*n - a(n-1) - 6 (with a(1) = 2). - Vincenzo Librandi, Aug 05 2010
a(n+1) = a(n) + (a(n) mod 6). - M. F. Hasler, Jan 14 2014
Sum_{n>=1} 1/a(n)^2 = Pi^2/27. - Dimitris Valianatos, Oct 10 2017
a(n) = (6*n - (-1)^n - 3)/2. - Ammar Khatab, Aug 23 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)). - Amiram Eldar, Dec 11 2021
E.g.f.: 2 + ((6*x - 3)*exp(x) - exp(-x))/2. - David Lovler, Aug 25 2022
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 2/sqrt(3) (10 * A020832).
Product_{n>=1} (1 + (-1)^n/a(n)) = 1/sqrt(3) (A020760). (End)

A029898 Pitoun's sequence: a(n+1) is digital root of a(0) + ... + a(n).

Original entry on oeis.org

1, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2

Offset: 0

Amela2(AT)aol.com

If the initial 1 is omitted, this is 2^n mod 9. - N. J. A. Sloane
From Cino Hilliard, Dec 31 2004: (Start)
Except for the initial term, also the digital root of 11^n.
Except for the initial term, also the decimal expansion of 125/1001.
Except for the initial term, also the digital root of 2^n. (End)
Aside from the first term, periodic with period 6. - Charles R Greathouse IV, Nov 29 2011

			1 + 1 + 2 + 4 + 8 + 7 + 5 = 28 -> 2 + 8 = 10 -> a(7) = 1.

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Cf. A007612, A010888.

a[n_] := PowerMod[2, n-1, 9]; a[0] = 1; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Nov 29 2011 *)
Join[{1},LinearRecurrence[{1,0,-1,1},{1,2,4,8},110]] (* or *) Join[{1}, PowerMod[2,Range[110],9]] (* Harvey P. Dale, Nov 24 2014 *)

a(n)=if(n,[5,1,2,4,8,7][n%6+1],1) \\ Charles R Greathouse IV, Nov 29 2011

[power_mod(2,n,9)for n in range(0, 105)] # Zerinvary Lajos, Nov 03 2009

a(n) = digital root of 2^(n-1) in base 10 = 2^(n-1) (mod 9). - Olivier Gérard, Jun 06 2001
For n > 0: a(n+6) = a(n) and a(n) = A007612(n+1) - A007612(n) = A010888(A007612(n)). - Reinhard Zumkeller, Feb 27 2006
a(n) = (9 + cos(n*Pi) - 4*sqrt(3)*sin(n*Pi/3))/2 for n > 0 with a(0)=1. - Wesley Ivan Hurt, Oct 04 2018
From Stefano Spezia, Jun 27 2022: (Start)
O.g.f.: (1 + x^2 + 3*x^3 + 4*x^4)/((1 - x)*(1 + x)*(1 - x + x^2)).
E.g.f.: 5*cosh(x) - 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) + 4*(sinh(x) - 1). (End)

More terms from Cino Hilliard, Dec 31 2004

A010077 a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10

Offset: 0

N. J. A. Sloane, Leonid Broukhis

The digital sum analog (in base 10) of the Fibonacci recurrence. - Hieronymus Fischer, Jun 27 2007
a(n) and Fibonacci(n) = A000045(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fibonacci(n) mod 9) = A007887(n). Thus (a(n) mod 9) is periodic with the Pisano period A001175(9)=24. - Hieronymus Fischer, Jun 27 2007
a(n) == A004090(n) (mod 9) (A004090(n) = digital sum of Fibonacci(n)). - Hieronymus Fischer, Jun 27 2007
For general bases p > 2, we have the inequality 2 <= a(n) <= 2p-3 (for n > 2). Actually, a(n) <= 17 = A131319(10) for the base p=10. - Hieronymus Fischer, Jun 27 2007

David A. Corneth, Table of n, a(n) for n = 0..9999
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A007612, A065076.
Cf. A000045, A010073, A010074, A010075, A010076.
Cf. A131294, A131295, A131296, A131297, A131318, A131319, A131320.

a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 1] ]] + Apply[ Plus, IntegerDigits[ a[n - 2] ]]; Table[ a[n], {n, 0, 100} ]
nxt[{a_,b_}]:={b, Total[IntegerDigits[a]]+Total[IntegerDigits[b]]}; NestList[ nxt,{0,1},80][[All,1]] (* Harvey P. Dale, Apr 15 2018 *)

first(n) = {n = max(n, 2); my(res = vector(n)); res[2] = 1; for(i = 3, n, res[i] = sumdigits(res[i-1]) + sumdigits(res[i-2]) ); res } \\ David A. Corneth, May 26 2021

Periodic from n=3 with period 24. - Franklin T. Adams-Watters, Mar 13 2006
a(n) = A030132(n-4) + A030132(n-3) for n>3. - Reinhard Zumkeller, Jul 04 2007
a(n) = a(n-1) + a(n-2) - 9*(floor(a(n-1)/10) + floor(a(n-2)/10)). - Hieronymus Fischer, Jun 27 2007
a(n) = floor(a(n-1)/10) + floor(a(n-2)/10) + (a(n-1) mod 10) + (a(n-2) mod 10). - Hieronymus Fischer, Jun 27 2007
a(n) = A059995(a(n-1)) + A059995(a(n-2)) + A010879(a(n-1)) + A010879(a(n-2)). - Hieronymus Fischer, Jun 27 2007
a(n) = Fibonacci(n) - 9*Sum_{k=2..n-1} Fibonacci(n-k+1)*floor(a(k)/10) where Fibonacci(n) = A000045(n). - Hieronymus Fischer, Jun 27 2007

A102039 a(n) = a(n-1) + last digit of a(n-1), starting at 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, 102, 104, 108, 116, 122, 124, 128, 136, 142, 144, 148, 156, 162, 164, 168, 176, 182, 184, 188, 196, 202, 204, 208, 216, 222, 224, 228, 236, 242, 244, 248, 256, 262, 264, 268, 276, 282

Offset: 1

Samantha Stones (devilsdaughter2000(AT)hotmail.com), Dec 25 2004

Sequence A001651 is the "base 3" version. In base 4 this rule leads to (1,2,4,4,4...), in base 5 to (1,2,4,8,11,12,14,18,21,22,24,28...) = A235700. - M. F. Hasler, Jan 14 2014

This and the following sequences (none of which is "base"!) could all be defined by a(1) = 1 and a(n+1) = a(n) + (a(n) mod b) with different values of b: A001651 (b=3), A235700 (b=5), A047235 (b=6), A047350 (b=7), A007612 (b=9). Using b=4 or b=8 yields a constant sequence from that term on. - M. F. Hasler, Jan 15 2014

			28 + 8 = 36, 36 + 6 = 42.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Apart from initial term, same as A002081.

LinearRecurrence[{2,-2,2,-1},{1,2,4,8,16},60] (* Harvey P. Dale, Jul 02 2022 *)

print1(a=1);for(i=1,99,print1(","a+=a%10)) \\ M. F. Hasler, Jan 14 2014

Vec(x*(5*x^4+2*x^3+2*x^2+1)/((x-1)^2*(x^2+1)) + O(x^100)) \\ Colin Barker, Sep 20 2014

a(n) = if(n==1, 1, (-10-(1-I/2)*(-I)^n-(1+I/2)*I^n+5*n)) \\ Colin Barker, Oct 18 2015

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>5. G.f.: x*(5*x^4+2*x^3+2*x^2+1) / ((x-1)^2*(x^2+1)). - Colin Barker, Sep 20 2014

a(n) = (-10 - (1-i/2)*(-i)^n - (1+i/2)*i^n + 5*n) for n>1, where i = sqrt(-1). - Colin Barker, Oct 18 2015

A065076 a(0) = 0, a(1) = 1, a(n) = (sum of digits of a(n-1)) + a(n-2).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 12, 16, 19, 26, 27, 35, 35, 43, 42, 49, 55, 59, 69, 74, 80, 82, 90, 91, 100, 92, 111, 95, 125, 103, 129, 115, 136, 125, 144, 134, 152, 142, 159, 157, 172, 167, 186, 182, 197, 199, 216, 208, 226, 218, 237, 230, 242, 238, 255, 250, 262, 260, 270

Offset: 0

Bodo Zinser, Nov 09 2001

			a(8) = 12 because a(7) = 13, a(6) = 8 and 4 = 1+3 and 12 = 4 + 8.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A007953 and A007612.

Cf. A030132.

a065076 n = a065076_list !! n
a065076_list = 0 : 1 : zipWith (+)
                a065076_list (map a007953 $ tail a065076_list)
-- Reinhard Zumkeller, Nov 13 2014

a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 1] ]] + a[n - 2]; Table[ a[n], {n, 0, 100} ]
Transpose[NestList[{Last[#],Total[IntegerDigits[Last[#]]]+First[#]}&, {0,1}, 60]][[1]] (* Harvey P. Dale, Dec 07 2011 *)

{ my(a,a1,a2); for (n=0, 60, if (n>1, a=sumdigits(a1) + a2; a2=a1; a1=a, if (n, a=a1=1, a=a2=0)); print1(a, ", ") ) } \\ Harry J. Smith, Oct 06 2009

More terms from Larry Reeves (larryr(AT)acm.org) and Robert G. Wilson v, Nov 13 2001

A235700 a(n+1) = a(n) + (a(n) mod 5), a(1)=1.

Original entry on oeis.org

1, 2, 4, 8, 11, 12, 14, 18, 21, 22, 24, 28, 31, 32, 34, 38, 41, 42, 44, 48, 51, 52, 54, 58, 61, 62, 64, 68, 71, 72, 74, 78, 81, 82, 84, 88, 91, 92, 94, 98, 101, 102, 104, 108, 111, 112, 114, 118, 121, 122, 124, 128, 131, 132, 134, 138, 141, 142, 144, 148, 151, 152, 154, 158, 161, 162, 164, 168, 171, 172, 174, 178, 181, 182, 184, 188, 191

Offset: 1

M. F. Hasler, Jan 14 2014

Although the present sequence has not been thought of via "writing a(n) in base b", this could be seen as "base 5" version of A102039 (base 10) and A001651 (base 3), A047235 (base 6), A047350 (base 7) and A007612 (base 9). For 4 or 8 one would get a sequence constant from that (3rd resp. 4th) term on.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Cf. A001651, A007612, A047235, A047350, A102039.

NestList[#+Mod[#,5]&,1,80] (* Harvey P. Dale, Oct 20 2024 *)

is_A235700(n) = bittest(278,n%10) \\ 278=2^1+2^2+2^4+2^8

PARI
```
A235700 = n -> 2^((n-1)%4)+(n-1)\4*10
```

print1(a=1);for(i=1,99,print1(","a+=a%5))

Vec(x*(2*x^3+2*x^2+1)/((x-1)^2*(x^2+1)) + O(x^100)) \\ Colin Barker, Jan 16 2014

a(n) = 2^(n-1 mod 4) + 10*floor((n-1)/4).
From Colin Barker, Jan 16 2014: (Start)
a(n) = (-10+(1+2*i)*(-i)^n+(1-2*i)*i^n+10*n)/4 where i=sqrt(-1).
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4).
G.f.: x*(2*x^3+2*x^2+1) / ((x-1)^2*(x^2+1)). (End)
E.g.f.: (4 + 5*exp(x)*(x - 1) + cos(x) + 2*sin(x))/2. - Stefano Spezia, Feb 22 2025

A065124 a(n) = (sum of digits of a(n-2)) + a(n-1); a(0) = 0 and a(1) = 1.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 25, 28, 35, 45, 53, 62, 70, 78, 85, 100, 113, 114, 119, 125, 136, 144, 154, 163, 173, 183, 194, 206, 220, 228, 232, 244, 251, 261, 269, 278, 295, 312, 328, 334, 347, 357, 371, 386, 397, 414, 433, 442, 452, 462, 473, 485, 499, 516

Offset: 0

Robert G. Wilson v, Nov 13 2001

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A007612, A007953, A065076.

Cf. A010888, A030132.

a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 2] ]] + a[n - 1]; Table[ a[n], {n, 0, 100} ]

{ for (n=0, 1000, if (n>1, a=sumdigits(a2) + a1; a2=a1; a1=a, if (n, a=a1=1, a=a2=0)); write("b065124.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 10 2009

A010888(a(n)) = A030132(n). - Davide Rotondo, Dec 02 2024

A229527 Start with 1, skip (sum of digits of n) numbers, accept next number.

Original entry on oeis.org

1, 3, 7, 15, 22, 27, 37, 48, 61, 69, 85, 99, 118, 129, 142, 150, 157, 171, 181, 192, 205, 213, 220, 225, 235, 246, 259, 276, 292, 306, 316, 327, 340, 348, 364, 378, 397, 417, 430, 438, 454, 468, 487, 507, 520, 528, 544, 558, 577, 597

Offset: 1

Dave Durgin, Sep 25 2013

			a(1)=1, a(2)=1+1+1=3, a(3)=3+3+1=7, a(4)=7+7+1=15, a(5)=15+1+5+1=22, a(6)=22+2+2+1=27, ...

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A007612, A004207, A160939.

a[n_] := a[n] = a[n - 1] + 1 + Plus @@ IntegerDigits@a[n - 1]; a[1] = 1; Array[a, 50] (* Robert G. Wilson v, Aug 01 2018 *)

from itertools import islice
def A229527_gen(): # generator of terms
    a = 1
    while True:
        yield a
        a += sum(map(int,str(a)))+1
A229527_list = list(islice(A229527_gen(),40)) # Chai Wah Wu, Aug 09 2025

a(n+1) = a(n) + (sum of digits of a(n)) + 1.

A176718 Partial sums of A004207.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 55, 83, 121, 170, 232, 302, 379, 470, 571, 674, 781, 896, 1018, 1145, 1282, 1430, 1591, 1760, 1945, 2144, 2362, 2591, 2833, 3083, 3340, 3611, 3892, 4184, 4489, 4802, 5122, 5447, 5782, 6128, 6487, 6863, 7255, 7661, 8077, 8504, 8944, 9392

Offset: 0

Jonathan Vos Post, Apr 25 2010

Partial sums of a(1) = 1, a(n) = sum of digits of all previous terms. The subsequence of primes in this sequence begins: 2, 83, 379, 571, 2591, 2833, 3083, 6863, 10831. The subsequence of squares in this sequence begins: 1, 4, 16, 121, 4489.

			a(7) = 1 + 1 + 2 + 4 + 8 + 16 + 23 + 28 = 83 is prime.

Cf. A004207, A016052, A033298, A007612.

A176718 := proc(n)
    add( A004207(k),k=0..n) ;
end proc: # R. J. Mathar, Apr 02 2014

a(n) = SUM[i=0..n] A004207(i) = SUM[i=0..n] {b(1) = 1, b(j) = sum of digits of b(j) for j = 0..i} = SUM[i=0..n] {b(1) = 1, b(k) = A007953(b(k)) for k = 0..i}.

cp's OEIS Frontend

A004207 a(0) = 1, a(n) = sum of digits of all previous terms.

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A047235 Numbers that are congruent to {2, 4} mod 6.

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A029898 Pitoun's sequence: a(n+1) is digital root of a(0) + ... + a(n).

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A010077 a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1.

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A102039 a(n) = a(n-1) + last digit of a(n-1), starting at 1.

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A065076 a(0) = 0, a(1) = 1, a(n) = (sum of digits of a(n-1)) + a(n-2).

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