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A274084
Triangular numbers that are repdigits with length > 2 in some base.
1
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
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
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jun 09 2016
STATUS
approved