A066568 -id:A066568 - 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

A243442 Primes p such that, in base 2, p - digitsum(p) is also a prime.

Original entry on oeis.org

5, 23, 71, 83, 101, 113, 197, 281, 317, 353, 359, 373, 401, 467, 599, 619, 683, 739, 751, 773, 977, 1091, 1097, 1103, 1217, 1223, 1229, 1237, 1283, 1303, 1307, 1429, 1433, 1489, 1553, 1559, 1601, 1607, 1613, 1619, 1699, 1873, 1879, 2039, 2347, 2357, 2389

Offset: 1

Anthony Sand, Jun 05 2014

In all bases b, x = n - digitsum(n) is always divisible by b-1, therefore x can be prime only in base 2 and bases b for which b-1 is prime. For example, in base 10, n - digitsum(n) is always divisible by 10 - 1 = 9 -- see A066568 and A068395. In base 8, 9 = 11, therefore 11 - digitsum(11) = 9 - 2 = 7 is divisible by 7.

			5 - digitsum(5,base=2) = 5 - digitsum(101) = 5 - 2 = 3.
23 - digitsum(10111) = 23 - 4 = 19.
71 - digitsum(1000111) = 71 - 4 = 67.
83 - digitsum(1010011) = 83 - 4 = 79.
101 - digitsum(1100101) = 101 - 4 = 97.

Anthony Sand, Table of n, a(n) for n = 1..1000

Cf. A243441.

Select[Prime[Range[400]],PrimeQ[#-Total[IntegerDigits[#,2]]]&] (* Harvey P. Dale, May 15 2019 *)

isok(n) = isprime(n) && isprime(n - hammingweight(n)); \\ Michel Marcus, Jun 05 2014

A171181 n followed by (n - sum of digits of n).

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 9, 11, 9, 12, 9, 13, 9, 14, 9, 15, 9, 16, 9, 17, 9, 18, 9, 19, 9, 20, 18, 21, 18, 22, 18, 23, 18, 24, 18, 25, 18, 26, 18, 27, 18, 28, 18, 29, 18, 30, 27, 31, 27, 32, 27, 33, 27, 34, 27, 35, 27, 36, 27, 37, 27, 38, 27, 39, 27

Offset: 0

Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Dec 04 2009

			a(0) = 0, a(1) = 0 - 0 = 0.
a(2) = 1, a(3) = 1 - 1 = 0.
a(4) = 2, a(5) = 2 - 2 = 0.
a(6) = 3, a(7) = 3 - 3 = 0.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Interspersion of A001477 and A066568.

Table[{n,n-Total[IntegerDigits[n]]},{n,0,40}]//Flatten (* Harvey P. Dale, Nov 26 2016 *)

a(n) = if (n % 2 == 0, n/2, nn = n\2; d = digits(nn); nn - sum(i=1, #d, d[i]);); \\ Michel Marcus, Aug 14 2013

If n is even, a(n) = n/2; if n is odd, a(n) = A066568(floor(n/2)). - Michel Marcus, Aug 14 2013

Edited by N. J. A. Sloane, Dec 05 2009

A229621 Numbers n such that n - (sum of digits of n) is a palindrome.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 420, 421, 422, 423, 424, 425, 426

Offset: 1

Derek Orr, Sep 26 2013

			185 - (1+8+5) = 171 (a palindrome). Thus, 185 is a member of this sequence.

Cf. A066568.

Select[Range[0,500],PalindromeQ[#-Total[IntegerDigits[#]]]&]

ispal(d) = Vecrev(d) == d;
isok(n) = ispal(digits(n-sumdigits(n))); \\ Michel Marcus, Apr 11 2015

def ispal(n):
  r = ''
  for i in str(n):
    r = i + r
  return n == int(r)
def DS(n):
  s = 0
  for i in str(n):
    s += int(i)
  return s
{print(n, end=', ') for n in range(10**3) if ispal(n-DS(n))}
## Simplified by Derek Orr, Apr 10 2015

More terms from Derek Orr, Apr 10 2015

A344853 a(n) = n minus (sum of digits of n in base 3).

Original entry on oeis.org

0, 0, 0, 2, 2, 2, 4, 4, 4, 8, 8, 8, 10, 10, 10, 12, 12, 12, 16, 16, 16, 18, 18, 18, 20, 20, 20, 26, 26, 26, 28, 28, 28, 30, 30, 30, 34, 34, 34, 36, 36, 36, 38, 38, 38, 42, 42, 42, 44, 44, 44, 46, 46, 46, 52, 52, 52, 54, 54, 54, 56, 56, 56, 60, 60, 60, 62, 62, 62

Offset: 0

Thomas König, May 30 2021

All terms are even.

In all sequences of the form f(n) = n minus (sum of digits of n in base b), every term appears b times consecutively. Here b = 3, hence terms are entries of A346502 repeated 3 times. - Bernard Schott, Jul 21 2021

			a(20) = 20 - (2 + 0 + 2) = 16 because 20 is written as 202 in base 3.

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A011371 (in base 2), A066568 (in base 10).

Cf. A004128, A053735, A054861, A346502.

a[n_] := n - Plus @@ IntegerDigits[n, 3]; Array[a, 70, 0] (* Amiram Eldar, May 30 2021 *)

a(n) = n - sumdigits(n, 3); \\ Michel Marcus, Jul 11 2021

a(n) = n - A053735(n).
a(n) = 2 * A054861(n).
a(n) = 2 * A004128(floor(n/3)).
a(3*n) = a(3*n+1) = a(3*n+2).

A356384 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) = x_n(b-1) minus the sum of digits of x_n(b-1) in base b; a(n) is the least b such that x_n(b) = 0.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13

Offset: 0

Rémy Sigrist, Aug 05 2022

This sequence is well defined: for any n >= 0: if x_n(b) > 0, then x_n(b+1) < x_n(b), and we must eventually reach 0.
This sequence is weakly increasing; this is related to the fact that for any base b > 1, k -> (k minus the sum of digits of k in base b) is weakly increasing.
Note that some values (like 7) do not appear in this sequence (see also A356386).

			For n = 42:
- we have:
      b  x(b)
      -  ----
      1    42
      2    39
      3    36
      4    33
      5    28
      6    20
      7    12
      8     7
      9     0
- so a(42) = 9.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, Colored scatterplot of (n, x_n(b)) for n <= 1000 and b = 1..a(n) (the color is function of b)
Rémy Sigrist, PARI program

Cf. A011371, A066568, A071542, A261231, A344853, A356386.

PARI
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See Links section.
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A108638 Semiprime plus its digits is semiprime.

Original entry on oeis.org

15, 22, 26, 33, 38, 39, 49, 51, 55, 57, 74, 77, 115, 123, 129, 134, 145, 155, 161, 169, 178, 187, 202, 206, 213, 214, 221, 237, 254, 265, 274, 278, 291, 299, 301, 303, 309, 321, 327, 335, 361, 371, 377, 381, 382, 386, 411, 437, 445, 466, 478, 485, 497, 505

Offset: 1

Zak Seidov, Jun 14 2005

Members k of A001358 such that A062028(k) is in A001358. - Robert Israel, Oct 01 2024
Surprisingly there are only three(?) semiprimes sp, 10,14,15, such that sp minus its digits is semiprime.
That is because n - (sum of its digits) = A066568(n) is divisible by 9. - Robert Israel, Oct 01 2024

			15=3*5 and 15+1+5=21=3*7.

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

Cf. A001358, A062028, A066568.

filter:= n -> numtheory:-bigomega(n) = 2 and numtheory:-bigomega(n+convert(convert(n,base,10),`+`))=2:
select(filter, [$1..1000]); # Robert Israel, Oct 01 2024

Select[Range[500], Plus@@Last/@FactorInteger[ # ]==Plus@@Last/@FactorInteger[ #+Plus@@IntegerDigits[ # ]]==2&]

A225048 Numbers that cannot be expressed as n plus the sum of the squared digits of n for any integer n.

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 9, 10, 14, 15, 16, 18, 19, 21, 22, 25, 27, 28, 29, 32, 33, 34, 35, 37, 38, 40, 43, 46, 47, 48, 49, 50, 52, 55, 57, 60, 61, 63, 64, 65, 70, 71, 73, 74, 78, 79, 82, 84, 85, 88, 89, 91, 92, 93, 94, 97, 99, 100, 104, 106, 109, 110, 115, 120, 122

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 25 2013

A natural extension of the Self or Colombian numbers (A003052).

Up to 144, there are more numbers that cannot be expressed in this way than numbers that can. Thereafter, there are always more numbers that can.

			26 is not in the sequence, because 21+2^2+1^2=26. However, no such solution exists for 25 or 27.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Cf. A003052, A003219, A003132, A062028, A066568.

nn=122;Complement[Range[nn],Table[n+Total[IntegerDigits[n]^2],{n,nn}]] (* Jayanta Basu, May 05 2013 *)

digsqsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2)
which(is.na(match(1:1000,1:1000+sapply(1:1000,digsqsum)))

A225049 Numbers that can be expressed as n plus sum of squared digits(n) in more than one way.

Original entry on oeis.org

30, 41, 56, 81, 95, 96, 98, 101, 112, 114, 121, 125, 131, 142, 146, 152, 157, 168, 173, 177, 182, 186, 191, 196, 197, 199, 206, 209, 213, 215, 216, 217, 227, 230, 232, 234, 240, 243, 245, 247, 248, 257, 260, 262, 266, 272, 276, 284, 285, 287, 292, 299, 300

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 25 2013

			a(13) = 131 is included because 131 = 57+5^2+7^2 = 73+7^2+3^2 = 105+1^2+5^2 = 122 + 1^2+4^2+4^2.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, All the integers that yield a(n) for n=1..10000

Cf. A225048, A003052, A003219, A003132, A062028, A066568.

digsqsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2)
1:500+sapply(1:500,digsqsum)->y
table(y)->ty; names(ty[ty>1])

A244573 Numbers n such that 10n + d - digsum(10n + d) is a palindrome for any d in {0,1,2,3,4,5,6,7,8,9}.

Original entry on oeis.org

1, 10, 18, 26, 34, 42, 68, 76, 84, 92, 100, 279, 368, 457, 546, 635, 724, 813, 902, 1000, 1071, 1152, 1233, 1314, 1486, 1567, 1648, 1729, 1981, 2051, 2132, 2213, 2385, 2466, 2547, 2628, 2709, 2880, 2961, 3031, 3112, 3284, 3365, 3446, 3527, 3608, 3699, 3860, 3941, 4011, 4183, 4264

Offset: 1

Derek Orr, Jun 30 2014

			180 - (1+8+0) = 171, a palindrome. By adding {1,2,3,4,5,6,7,8,9} to 180 and subtracting that number's digsum, it will still be 171, a palindrome. Since 180 = 18*10, 18 is a member of this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A229621, A066568.

palQ[n_]:=AnyTrue[Table[10n+d-Total[IntegerDigits[10n+d]],{d,0,9}],PalindromeQ]; Select[Range[4300],palQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 13 2021 *)

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,10^4,s=sum(i=1,#digits(10*n),digits(10*n)[i]);if(rev(10*n-s)==10*n-s,print1(n,", ")))

cp's OEIS Frontend

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

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A243442 Primes p such that, in base 2, p - digitsum(p) is also a prime.

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A171181 n followed by (n - sum of digits of n).

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A229621 Numbers n such that n - (sum of digits of n) is a palindrome.

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A344853 a(n) = n minus (sum of digits of n in base 3).

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A356384 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) = x_n(b-1) minus the sum of digits of x_n(b-1) in base b; a(n) is the least b such that x_n(b) = 0.

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A108638 Semiprime plus its digits is semiprime.

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A244573 Numbers n such that 10n + d - digsum(10n + d) is a palindrome for any d in {0,1,2,3,4,5,6,7,8,9}.