A320870 Irregular table: row n >= 0 lists numbers m >= 0 such that n = A062028(m) := m + sum of digits of m.

0, 1, 2, 3, 4, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, 15, 20, 16, 21, 17, 22, 18, 23, 19, 24, 25, 30, 26, 31, 27, 32, 28, 33, 29, 34, 35, 40, 36, 41, 37, 42, 38, 43, 39, 44, 45, 50, 46, 51, 47, 52, 48, 53, 49, 54, 55, 60, 56, 61, 57, 62, 58, 63, 59, 64, 65, 70, 66, 71, 67, 72, 68, 73, 69, 74, 75, 80, 76, 81, 77, 82, 78, 83, 79, 84, 85, 90

Offset: 0

Author

M. F. Hasler, Nov 09 2018

Keywords

• nonn
• tabf
• base

Comments

Row lengths are given by A230093.

Examples

			The first nonempty rows are:
    n  | list of m
    0  | 0        // since 0 = 0 + 0
    2  | 1        // since 2 = 1 + 1
    4  | 2        // etc.
    6  | 3        // Below 10 every odd row is empty, but thereafter,
    8  | 4        // only rows 20, 31, 42, ..., 108 (steps of 11),
   10  | 5        // 110, 121, 132, ..., 198, etc. are empty.
   11  | 10       // Since 11 = 10 + (1 + 0)
   12  | 6
   13  | 11       // The first prime that yields a prime: 11 + (1 + 1) = 13.
     (...)
  100  | 86       // The first row of length 2 is 101:
  101  | 91, 100  // 101 = 91 + (9 + 1) = 100 + (1 + 0 + 0)
  102  | 87
     (...)
		

Links

• Robert Israel, Table of n, a(n) for n = 0..9971 (rows 0 to 10000, flattened)

Crossrefs

Cf. A007953 (sum of digits of n), A062028 (n + digit sum of n).

Cf. A230093 (number of m such that m + (sum of digits of m) is n).

Cf. A006064 (least m with row length n),

Cf. A003052 (Self or Colombian numbers: rows of length 0), A006378 (Colombian primes).

Cf. A320881 (indices of rows containing a prime), A048520 (primes among these).

Programs

Maple

N:= 100: # for rows 0 to N, flattened
for i from 0 to N do V[i]:= NULL od:
for i from 0 to N-1 do
  v:= convert(convert(i,base,10),`+`);
  if v <= N then V[v]:= V[v],i fi
od:
seq(V[i],i=1..N); # Robert Israel, Jul 21 2025

PARI

A320870_row(n)=if(n,select(m->m+sumdigits(m)==n,[max(n-9*logint(n,10)+8,n\/2)..n-1]),[0])