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A069790 Triangular numbers with arithmetic mean of digits = 1 (sum of digits = number of digits). 2
1, 120, 210, 300, 112101, 100600020, 101111310, 110120220, 200130021, 200310120, 1000051003, 1010004040, 1130002030, 1411000003, 2002021003, 3200200003, 5000050000, 100110002070, 111111101310, 111202101003, 180000300000, 211104100200, 231201020001, 500001500001, 501001000500, 100021000424010 (list; graph; refs; listen; history; text; internal format)
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)
Suppose A007953(x) + A007953(2*x^2) - A055642(2*x^2) is even and
A007953(x) + A007953(2*x^2) >= 2*A055642(x) + A055642(2*x^2).
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
Sequence in context: A056994 A288461 A114823 * A064224 A069674 A003015
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

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Last modified February 23 21:40 EST 2024. Contains 370288 sequences. (Running on oeis4.)