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

1,1

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.

Links

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

Example

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

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));

Crossrefs

Cf. A000217, A045914, A167782.

Sequence in context: A119101 A342806 A190662 * A350098 A334118 A219918

Adjacent sequences: A274081 A274082 A274083 * A274085 A274086 A274087

Keyword

nonn,base

Author

Robert Israel, Jun 09 2016

Status

approved