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

%I #11 Jul 20 2020 13:11:10

%S 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,

%T 30,26,31,27,32,28,33,29,34,35,40,36,41,37,42,38,43,39,44,45,50,46,51,

%U 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

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

%C Row lengths are given by A230093.

%e The first nonempty rows are:

%e n | list of m

%e 0 | 0 // since 0 = 0 + 0

%e 2 | 1 // since 2 = 1 + 1

%e 4 | 2 // etc.

%e 6 | 3 // Below 10 every odd row is empty, but thereafter,

%e 8 | 4 // only rows 20, 31, 42, ..., 108 (steps of 11),

%e 10 | 5 // 110, 121, 132, ..., 198, etc. are empty.

%e 11 | 10 // Since 11 = 10 + (1 + 0)

%e 12 | 6

%e 13 | 11 // The first prime that yields a prime: 11 + (1 + 1) = 13.

%e (...)

%e 100 | 86 // The first row of length 2 is 101:

%e 101 | 91, 100 // 101 = 91 + (9 + 1) = 100 + (1 + 0 + 0)

%e 102 | 87

%e (...)

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

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

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

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

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

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

%K nonn,tabf,base

%O 0,3

%A _M. F. Hasler_, Nov 09 2018