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

0,3

Comments

Row lengths are given by A230093.

Links

Table of n, a(n) for n=0..86.

Example

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
     (...)

Prog

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

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).

Sequence in context: A302840 A357082 A360521 * A252022 A039697 A319131

Adjacent sequences: A320867 A320868 A320869 * A320871 A320872 A320873

Keyword

nonn,tabf,base

Author

M. F. Hasler, Nov 09 2018

Status

approved