A048347 -id:A048347 - cp's OEIS frontend

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

Patrick De Geest, Mar 15 1999

Eric Weisstein's World of Mathematics, Triangular Number

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

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 *)

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

A036509 Smallest square containing exactly n 2's.

Original entry on oeis.org

25, 225, 22201, 2002225, 21022225, 212722225, 11222224225, 132922222225, 12222722202201, 22222220262025, 1222522204222225, 22292262226224225, 2222262262926922225, 22226224222205212225, 2222222222222640225, 22222262422274682222225, 1222212242622225512222224, 2220022223125222222222201

Offset: 1

David W. Wilson

a(21) > 10^28. - Giovanni Resta, Jul 27 2018

Giovanni Resta, Table of n, a(n) for n = 1..20

Cf. A048347. - Jon E. Schoenfield, Jan 24 2009

a[n_] := Block[{k=1}, While[DigitCount[k^2, 10, 2] != n, k++]; k^2]; Array[a, 7] (* Giovanni Resta, Jul 27 2018 *)

a(n) = A048347(n)^2. - Max Alekseyev, Oct 20 2008

a(13)-a(15) from Max Alekseyev, Oct 20 2008, Nov 10 2008, Dec 05 2008

a(16)-a(18) from Jon E. Schoenfield, Dec 25 2008

cp's OEIS Frontend

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

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