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a(n) is the index of the smallest triangular number containing exactly n 1's.
1

%I #21 Feb 19 2024 01:55:16

%S 1,18,58,458,1541,6018,47141,149406,471404,4756366,15563541,149075893,

%T 149004101,149071198,14907133333,47322533981,471406654834,

%U 1510636363333

%N a(n) is the index of the smallest triangular number containing exactly n 1's.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>

%t nsmall = Table[Infinity, 20];

%t For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];

%t n0 = Count[IntegerDigits[p], 1];

%t If[nsmall[[n0]] > i, nsmall[[n0]] = i]];

%t ReplaceAll[nsmall, Infinity -> "?"] (* _Robert Price_, Mar 22 2020 *)

%Y Cf. A036518, A048355-A049364.

%K nonn,base,more

%O 1,2

%A _Patrick De Geest_, Mar 15 1999

%E a(15)-a(16) from _Lars Blomberg_, May 13 2011

%E a(17)-a(18) from _Giovanni Resta_, Oct 30 2019