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%I #25 Apr 14 2022 15:18:30
%S 9,1,997,6,7,994,9999993,1,1,999981,1,9999999961,951,961,9999931,
%T 999999999999921,1,1,99999999801,1,99999999999999601,99501,99601,
%U 99999999301,99999999999999999999201,1,1,9999999999998001,1,999999999999999999996001,9995001,9996001
%N a(n) is the least term of the first run of A331786(n) consecutive numbers whose sum of digits (A007953) is not divisible by n.
%C A331786(n) is the number of consecutive integers in the largest such possible run.
%C Numbers k for which a(k) = 1 are in A352317.
%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a3-nombres-remarquables/5026-a389-les-decaxphobes">A389 - Les décaXphobes</a> (in French).
%F a(n) = A352689(n) - A331786(n) + 1 for n >= 2.
%F a(n) = 1 if n = 9*s, s > 0 (A008591), but the converse is not true.
%e a(4) = 997 because the A331786(4) = 6 consecutive numbers 997, 998, 999, 1000, 1001, 1002 have respectively sum of digits = 25, 26, 27, 1, 2, 3 and none is divisible by 4, and there is no smaller m < 997 such that sum of digits of m, m+1, m+2, m+3, m+4, m+5 is not divisible by 4.
%o (PARI) a(n) = my(t=gcd(n%9, 9)); if(t<9, 10^lift(Mod(-1, n/t)/(9/t)) - 10^(n\9)*(n%9-t+1) + 1, 1); \\ _Jinyuan Wang_, Mar 28 2022
%Y Cf. A007953, A008591, A331786, A331788, A352317, A352689.
%K nonn,base
%O 2,1
%A _Bernard Schott_, Mar 28 2022
%E More terms from _Jinyuan Wang_, Mar 28 2022
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