%I #13 Dec 27 2024 16:56:26
%S 2,2,2,2,2,2,2,10,11,6,7,11,11,4,11,9,10,29,24,29,29,29,29,29,36,28,
%T 83,69,79,110,56,83,110,72,164,236,119,178,299,209,218,308,216,416,
%U 596,506,277,443,579,589,1172,1217,991,1676,1779,2315,1325,1659,3125,2576
%N a(n) is the index of the smallest n-gonal number whose sum of digits is n.
%H Harvey P. Dale, <a href="/A359093/b359093.txt">Table of n, a(n) for n = 3..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%t p[n_, k_] := (n - 2)*k*(k - 1)/2 + k; a[n_] := Module[{k = 1}, While[Plus @@ IntegerDigits[p[n, k]] != n, k++]; k]; Array[a, 60, 3] (* _Amiram Eldar_, Dec 16 2022 *)
%t Table[Module[{k=1},While[Total[IntegerDigits[PolygonalNumber[n,k]]]!=n,k++];k],{n,3,70}] (* _Harvey P. Dale_, Dec 27 2024 *)
%Y Cf. A007953, A359003.
%K nonn,base
%O 3,1
%A _Ilya Gutkovskiy_, Dec 16 2022