cp's OEIS Frontend

A385905 Numbers k >= 1 such that digsum(k-r) + ... + digsum(k-1) = digsum(k+1) + ... + digsum(k+r) for some r >= 1 where digsum(i) is the digital sum of i (A007953).

%I A385905 #23 Aug 17 2025 08:22:15
%S A385905 9,10,19,20,29,30,39,40,49,50,59,60,69,70,77,79,80,85,86,89,90,91,92,
%T A385905 99,100,107,108,109,110,113,114,119,120,122,129,130,139,140,149,150,
%U A385905 159,160,169,170,177,179,180,185,186,189,190,191,192,197,199,200,202
%N A385905 Numbers k >= 1 such that digsum(k-r) + ... + digsum(k-1) = digsum(k+1) + ... + digsum(k+r) for some r >= 1 where digsum(i) is the digital sum of i (A007953).
%C A385905 Empirical observation: k != A214678(n).
%H A385905 Ctibor O. Zizka, <a href="/A385905/a385905.png">A385905 plot of k vs. r</a>
%e A385905 For k = 9: the least r = 8, A007953(1) + ... + A007953(8) = A007953(10) + ... + A007953(17), thus k = 9 is a term.
%t A385905 q[k_] := Module[{s = 0, r = 1}, While[r < k && (r == 1 || s != 0), s += (DigitSum[k-r] - DigitSum[k+r]); r++];1 < r <= k && s ==0]; Select[Range[202], q] (* _Amiram Eldar_, Aug 12 2025 *)
%Y A385905 Cf. A007953, A214678.
%K A385905 base,nonn
%O A385905 1,1
%A A385905 _Ctibor O. Zizka_, Aug 12 2025