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A210582 Numbers whose first digit is the remainder of their division by the last digit (in base 10).

%I A210582 #32 Sep 08 2022 08:46:01
%S A210582 13,19,23,26,29,39,46,49,59,69,79,89,103,109,127,133,163,193,197,199,
%T A210582 203,206,209,214,218,233,234,236,247,254,258,263,266,274,293,294,296,
%U A210582 298,299,309,367,399,406,409,417,428,436,466,468,487,496,499,509,537,599,609,638,657,678,699,709,799,809,899
%N A210582 Numbers whose first digit is the remainder of their division by the last digit (in base 10).
%C A210582 This is a restricted or simplified version of the definition of modest numbers A054986.
%H A210582 Reinhard Zumkeller, <a href="/A210582/b210582.txt">Table of n, a(n) for n = 1..10000</a>
%H A210582 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/NotModest.htm">Not Modest</a>, Mar 22 2012
%H A210582 E. Angelini, <a href="/A210582/a210582.pdf">Not modest</a> [Cached copy, with permission]
%F A210582 a(n) mod A010879(a(n)) = A000030(a(n)). [_Reinhard Zumkeller_, Mar 26 2011]
%o A210582 (PARI) is_nm( x )=x%10 && x%(x%10)==x\10^(#Str(x)-1)
%o A210582 for(n=1,999,is_nm(n)&print1(n","))
%o A210582 (Haskell)
%o A210582 a210582 n = a210582_list !! (n-1)
%o A210582 a210582_list = filter (\x -> mod x (a010879 x) == a000030 x) a067251_list
%o A210582 -- _Reinhard Zumkeller_, Mar 26 2012
%o A210582 (Magma) [ n: n in [1..1002] | not IsZero(d[1]) and n mod d[1] eq d[#d] where d is Intseq(n) ];  // _Bruno Berselli_, Mar 26 2012
%Y A210582 Cf. A054986, A178158.
%Y A210582 A subsequence of A067251, disjoint with A034709.
%K A210582 nonn,base
%O A210582 1,1
%A A210582 _Eric Angelini_ and _M. F. Hasler_, Mar 22 2012
%E A210582 Edited by _M. F. Hasler_, Jan 14 2014