A064806 -id:A064806 - cp's OEIS frontend

A062028 a(n) = n + sum of the digits of n.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 77

Offset: 0

Amarnath Murthy, Jun 02 2001

a(n) = A248110(n,A007953(n)). - Reinhard Zumkeller, Oct 01 2014

			a(34) = 34 + 3 + 4 = 41, a(40) = 40 + 4 = 44.

Harry J. Smith and N. J. A. Sloane, Table of n, a(n) for n = 0..10000 (first 1000 terms were computed by Harry J. Smith)
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A006378, A048521, A107740, A066568, A064806, A176995 (range), A003052, A230093, A248110.
Indices of: A047791 (primes), A107743 (composites), A066564 (squares), A084661 (cubes).
Iterations: A004207 (start=1), A016052 (start=3), A007618 (start=5), A006507 (start=7), A016096 (start=9).

a062028 n = a007953 n + n  -- Reinhard Zumkeller, Oct 11 2013

with(numtheory): for n from 1 to 100 do a := convert(n,base,10):
c := add(a[i],i=1..nops(a)): printf(`%d,`,n+c); od:
A062028 := n -> n+add(i,i=convert(n,base,10)) # M. F. Hasler, Nov 08 2018

Table[n + Total[IntegerDigits[n]], {n, 0, 100}]

A062028(n)=n+sumdigits(n) \\ M. F. Hasler, Jul 19 2015

def a(n): return n + sum(map(int, str(n)))
print([a(n) for n in range(71)]) # Michael S. Branicky, Jan 09 2023

a(n) = n + A007953(n).

a(n) = A160939(n+1) - 1. - Filip Zaludek, Oct 26 2016

More terms from Vladeta Jovovic, Jun 05 2001

A007612 a(n+1) = a(n) + digital root (A010888) of a(n).

Original entry on oeis.org

1, 2, 4, 8, 16, 23, 28, 29, 31, 35, 43, 50, 55, 56, 58, 62, 70, 77, 82, 83, 85, 89, 97, 104, 109, 110, 112, 116, 124, 131, 136, 137, 139, 143, 151, 158, 163, 164, 166, 170, 178, 185, 190, 191, 193, 197, 205, 212, 217, 218, 220, 224, 232, 239, 244, 245, 247, 251

Offset: 1

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Take m, a natural number. If m == 1 (mod 6), then for every n a(m)*a(n) is in A007612. - Ivan N. Ianakiev, May 08 2013

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).

T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Digital Root.

Cf. A004207, A010888, A029898, A064806.

a007612 n = a007612_list !! (n-1)
a007612_list = iterate a064806 1  -- Reinhard Zumkeller, Apr 13 2013

A007612 := proc(n) option remember: if(n=1)then return 1: fi: return procname(n-1) + ((procname(n-1)-1) mod 9) + 1: end: seq(A007612(n), n=1..100); # Nathaniel Johnston, May 04 2011

dr[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]; NestList[#+dr[#]&, 1,60] (* Harvey P. Dale, Sep 24 2011 *)
NestList[#+Mod[#,9]&,1,60] (* Harvey P. Dale, Sep 14 2016 *)

first(n)=my(v=vector(n)); v[1]=1; for(k=2,n, v[k]=v[k-1]+v[k-1]%9); v \\ Charles R Greathouse IV, Jun 25 2017

a(n)=n\6*27 + [-4,1,2,4,8,16][n%6+1] \\ Charles R Greathouse IV, Jun 25 2017

a(1) = 1, a(n+1) = a(n) + a(n) mod 9. - Reinhard Zumkeller, Mar 23 2003
First differences are [1,2,4,8,7,5] repeated. - M. F. Hasler, Sep 15 2009; corrected by John Keith, Aug 17 2022
n == 1, 2, 4, 8, 16, or 23 (mod 27). - Dean Hickerson, Mar 25 2003
Limit_{n->oo} a(n)/n = 9/2; A029898(n) = a(n+1) - a(n) = A010888(a(n)). - Reinhard Zumkeller, Feb 27 2006
a(6n+1)=27n+1, a(6n+2)=27n+2, a(6n+3)=27n+4, a(6n+4)=27n+8, a(6n+5)=27n+16, a(6n+6)=27n+23. - Franklin T. Adams-Watters, Mar 13 2006
G.f.: (1+4*x^4+3*x^3+x^2)/((x+1)*(x^2-x+1)*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009
a(n+1) = A064806(a(n)). - Reinhard Zumkeller, Apr 13 2013

A108773 Concatenation of n and the sum of the digits of n.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 112, 123, 134, 145, 156, 167, 178, 189, 1910, 202, 213, 224, 235, 246, 257, 268, 279, 2810, 2911, 303, 314, 325, 336, 347, 358, 369, 3710, 3811, 3912, 404, 415, 426, 437, 448, 459, 4610, 4711, 4812, 4913, 505, 516, 527

Offset: 0

N. J. A. Sloane, Jun 26 2005

A136614(n) = A007953(a(n)) = A007953(A136613(n)). - Reinhard Zumkeller, Jan 13 2008

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A108203, A062028, A064806.

Cf. A007953.

f[n_] := FromDigits[ Join[ IntegerDigits[n], IntegerDigits[Plus @@ IntegerDigits[n]]]]; Table[ f[n], {n, 0, 52}] (* Robert G. Wilson v, Jun 28 2005 *)

a(n) = eval(concat(Str(n), Str(sumdigits(n)))); \\ Michel Marcus, Nov 12 2023

More terms from Robert G. Wilson v, Jun 28 2005

A177274 Periodic sequence: Repeat 1, 2, 3, 4, 5, 6, 7, 8, 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6

Offset: 0

Klaus Brockhaus, May 07 2010

Interleaving of A131669 and A131669 without first five terms.
Continued fraction expansion of (684125+sqrt(635918528029))/1033802.
Decimal expansion of 13717421/111111111.
a(n) = A010888(n+1) = A010878(n)+1 = A117230(n+2)-1.
a(n) = A064806(n+1)-n-1.
Essentially first differences of A037123.

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

Cf. A131669 (odd digits followed by positive even digits), A010888 (digital root of n), A010878 (n mod 9), A117230 (1 followed by (repeat 2, 3, 4, 5, 6, 7, 8, 9, 10), offset 1), A064806 (n + digital root of n), A037123, A177270 (decimal expansion of (684125+sqrt(635918528029))/1033802).

&cat[ [1, 2, 3, 4, 5, 6, 7, 8, 9]: k in [1..12] ];

PadRight[{},120,Range[9]] (* Paolo Xausa, Jan 08 2024 *)

a(n) = (n mod 9)+1.
a(n) = a(n-9) for n > 8; 1; a(n) = n+1 for n <= 8.
G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8)/(1-x^9). [corrected by Georg Fischer, May 11 2019]

A108203 Numbers n put into lexicographical order which are the concatenation of k and the sum of the digits of k.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 112, 123, 134, 145, 156, 167, 178, 189, 202, 213, 224, 235, 246, 257, 268, 279, 303, 314, 325, 336, 347, 358, 369, 404, 415, 426, 437, 448, 459, 505, 516, 527, 538, 549, 606, 617, 628, 639, 707, 718, 729, 808, 819, 909, 1001

Offset: 1

Eric Angelini and Robert G. Wilson v, Jun 15 2005

			1 --> 11, 2 --> 22, 3 --> 33, ..., 9 --> 99, 10 --> 101, 11 --> 112, 12 --> 123,
..., 18 --> 189, 19 --> 1910 (ouch!), 20 --> 202, 21 --> 213, ...

Cf. A062028, A064806. Equals A108773 sorted.

f[n_] := FromDigits[ Join[ IntegerDigits[ n], IntegerDigits[Plus @@ IntegerDigits[ n]] ]]; t = {}; Do[t = Union[AppendTo[t, f[n]]], {n, 10^6}]

a(55) from Rémy Sigrist, May 16 2019

A253610 Numbers n with property that the sum of n and the digital root of n is prime.

Original entry on oeis.org

1, 10, 11, 13, 14, 16, 28, 29, 32, 34, 35, 46, 49, 52, 53, 65, 67, 68, 71, 82, 85, 89, 100, 101, 103, 104, 106, 122, 124, 136, 137, 142, 143, 155, 158, 160, 172, 175, 176, 190, 191, 193, 194, 209, 215, 226, 227, 229, 232, 233, 247, 250, 262, 265, 266, 269, 280

Offset: 1

Robert Gelhar, Jan 05 2015

Indices of primes in A064806. - Tom Edgar, Jan 07 2015

For any prime p >= 11, if p == k mod 9 then n = p - k/2 (if k is even) or p - (k+9)/2 (if k is odd) is in the sequence. - Robert Israel, Jan 07 2015

Cf. A010888, A064806.

[n: n in [1..300]| IsPrime(n+(1+(n-1)mod 9))]; // Vincenzo Librandi, Jan 15 2015

map(p -> p - (p/2 mod 9), [2, seq(ithprime(i), i=5..100)]); # Robert Israel, Jan 07 2015

Select[Range[100],PrimeQ[#+Mod[#,9]]&] (* Ivan N. Ianakiev, Feb 01 2015 *)

[n for n in [1..200] if is_prime(n+(1+(n-1)%9))] # Tom Edgar, Jan 05 2015

cp's OEIS Frontend

A062028 a(n) = n + sum of the digits of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

Extensions

A007612 a(n+1) = a(n) + digital root (A010888) of a(n).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

PARI

Formula

A108773 Concatenation of n and the sum of the digits of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A177274 Periodic sequence: Repeat 1, 2, 3, 4, 5, 6, 7, 8, 9.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A108203 Numbers n put into lexicographical order which are the concatenation of k and the sum of the digits of k.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A253610 Numbers n with property that the sum of n and the digital root of n is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Maple

Mathematica

Sage