A274084 Triangular numbers that are repdigits with length > 2 in some base.

15, 21, 91, 171, 666, 703, 820, 1830, 1953, 3003, 3081, 4095, 7140, 7381, 10440, 12720, 14706, 16471, 16653, 18915, 23871, 24976, 30628, 47586, 47895, 48828, 66430, 71631, 79401, 95703, 101475, 104653, 119805, 128778, 148240, 148785, 173166, 191271, 221445

Offset: 1

Author

Robert Israel, Jun 09 2016

Keywords

• nonn
• base

Comments

Intersection of A000217 and A167782.

Sequence is infinite, e.g. for any k>=2 and j>=1 it contains n*(n+1)/2 where n = ((8j+1)^k-1)/2: this has 2k digits of j in base 8j+1.

Examples

			15 = 5*6/2 = 1111_2.
21 = 6*7/2 = 111_4.
91 = 13*14/2 = 111_9.
171 = 18*19/2 = 333_7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..694

Crossrefs

Cf. A000217, A045914, A167782.

Programs

Maple

N:= 10^9: # to get all entries <= N
S:= {}:
for b from 2 to floor(sqrt(N)) do
  for k from 3 do
     r:= (b^k-1)/(b-1);
     if r > N then break fi;
     for a from 1 to min(b-1, N/r) do
        if issqr(1+8*r*a) then
          S:= S union {r*a}
        fi
     od
  od
od:
sort(convert(S,list));