A048364 a(n) is the index of the smallest triangular number containing exactly n 9's.
13, 44, 631, 1413, 28282, 76419, 282842, 1414213, 4471955, 31616419, 446313656, 1414001413, 6276925986, 44710913656, 44721356419, 632129732586, 527257052109, 14141923468538, 44698881216419, 199449241362306, 141421356237309, 4690415742340969, 42426404749855955, 44703449755024186, 1095435073375871053
Offset: 1
Links
- Eric Weisstein's World of Mathematics, Triangular Number
Crossrefs
Programs
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Mathematica
nsmall = Table[Infinity, 20]; For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i]; n0 = Count[IntegerDigits[p], 9]; If[nsmall[[n0]] > i, nsmall[[n0]] = i]]; ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)
Extensions
a(13)-a(15) from Lars Blomberg, May 16 2011
a(16)-a(18) from Giovanni Resta, Oct 30 2019
a(19)-a(25) from Max Alekseyev, Mar 07 2025