OFFSET
1,2
COMMENTS
The sum of the digits of a triangular number is 0, 1, 3 or 6 (mod 9).
From Robert Israel, Aug 24 2018: (Start)
Then 10^k*x*(1+2*10^k*x) is in the sequence, where k = (A007953(x) + A007953(2*x^2) - A055642(2*x^2))/2.
In particular, x = 10^j-2 satisfies this criterion for all j>=1, with k = j. Thus the sequence is infinite. - Robert Israel, Aug 24 2018
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..341 (all terms < 10^23)
MAPLE
T:= proc(n, k) option remember;
if n*9 < k then return {} fi;
if n = 1 then return {k} fi;
`union`(seq(map(t -> 10*t+j, procname(n-1, k-j)), j=0..min(9, k)))
end proc:
T(1, 0):= {}:
sort(convert(select(t -> issqr(8*t+1), `union`(seq(seq(T(9*i+j, 9*i+j), j=[0, 1, 3, 6]), i=0..1))), list)); # Robert Israel, Aug 24 2018
MATHEMATICA
s=Select[Range[500000], Length[z=IntegerDigits[ #(#+1)/2]]==Plus@@z&]; s(s+1)/2
Select[Accumulate[Range[500000]], Mean[IntegerDigits[#]]==1&] (* Harvey P. Dale, May 05 2011 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 08 2002
EXTENSIONS
Edited by Dean Hickerson and Robert G. Wilson v, Apr 10 2002
More terms from Robert Israel, Aug 24 2018
STATUS
approved