A048357 a(n) is the index of the smallest triangular number containing exactly n 2's.

6, 49, 215, 651, 6651, 66367, 206020, 635959, 6651759, 21411348, 66651759, 666816649, 666651759, 6666651759, 64687340681, 210818509825, 1115546688777, 6666665142651, 21411315850840, 66642647340651, 494412868404984, 2108185106684051, 21083748539063076, 209872546190692806, 494534695369742950

Offset: 1

Author

Patrick De Geest, Mar 15 1999

Keywords

• nonn
• base

Links

• Eric Weisstein's World of Mathematics, Triangular Number

Crossrefs

Cf. A036519, A048347, A048355, A048356, A048358, A048359, A048360, A048361, A048362, A048363, A048364, A048533.

Programs

Mathematica

nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 2];
  If[nsmall[[n0]] > i, nsmall[[n0]] = i]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(14)-a(15) from Lars Blomberg, May 13 2011

a(16)-a(18) from Giovanni Resta, Oct 30 2019

a(19)-a(25) from Max Alekseyev, Mar 07 2025