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

Author

Patrick De Geest, Mar 15 1999

Keywords

• nonn
• base

Links

• Eric Weisstein's World of Mathematics, Triangular Number

Crossrefs

Cf. A036526, A048354, A048355, A048356, A048357, A048358, A048359, A048360, A048361, A048362, A048363, A048547.

Programs

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