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A307560 a(n) = smallest m such that A307629(m) = n.

%I A307560 #39 Sep 08 2022 08:46:21
%S A307560 0,10,11,12,13,14,15,16,17,18,19,29,39,49,59,69,79,89,99,
%T A307560 10000000000000000000,109,1006,119,100000000000000000000000,129,
%U A307560 100004,139,1008,149,100000000000000000000000000000,159,10000000000000000000000000000000,169,1019,179,100006
%N A307560 a(n) = smallest m such that A307629(m) = n.
%H A307560 Arran Ireland, <a href="/A307560/b307560.txt">Table of n, a(n) for n = 0..304</a> (a(0) inserted by _Georg Fischer_, May 05 2019)
%H A307560 Arran Ireland, <a href="/A307560/a307560_1.txt">Python program</a> (a(0) inserted by _Georg Fischer_, May 05 2019)
%H A307560 Reddit website, <a href="http://old.reddit.com/r/math/comments/bd41rc/integer_sequence_pairwise_combinatorial_digit_sum">Integer sequence: Pairwise Combinatorial Digit Sum</a>
%F A307560 Let d be the smallest divisor of n for which 9*d*(d+1) >= n; then a(n) is the smallest (d+1)-digit number whose digit sum is n/d. - _Jon E. Schoenfield_, Apr 15 2019
%e A307560 a(39) = 1039 as (1 + 0) + (1 + 3) + (1 + 9) + (0 + 3) + (0 + 9) + (3 + 9) = 39. The sums in brackets are pairs of digits of 1039. No positive integer less than 1039 has this pairwise digit sum. - _David A. Corneth_, Apr 16 2019
%t A307560 fs[nd_, s_] := If[nd*9 < s, 0, Block[{n=10^(nd-1), f=0}, While[n < 10^nd, If[Total@ IntegerDigits@ n == s, f = n; Break[], n++]]; f]]; a[n_] := Block[{s}, Do[s = fs[d+1, n/d]; If[s > 0, Break[]], {d, Divisors[n]}]; s];  Join[{0}, Array[a,50]] (* _Giovanni Resta_, Apr 15 2019 *)
%o A307560 (Magma) for n in [1..50] do for d in Divisors(n) do if n le 9*d*(d+1) then nd:=d+1; sdLeft:=n div d; S:=[]; for j in [1..nd-1] do if sdLeft gt 9 then S[j]:=9; else S[j]:=sdLeft-1; end if; sdLeft-:=S[j]; end for; S[nd]:=sdLeft; a:=Seqint(S); n, a; break; end if; end for; end for; // _Jon E. Schoenfield_, Apr 15 2019
%Y A307560 Cf. A051885, A179239, A307629.
%K A307560 nonn,base
%O A307560 0,2
%A A307560 _Arran Ireland_, Apr 14 2019