login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069790 Triangular numbers with arithmetic mean of digits = 1 (sum of digits = number of digits). 1
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

Table of n, a(n) for n=1..26.

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

Cf. A007953, A055642.

Sequence in context: A056994 A288461 A114823 * A064224 A069674 A003015

Adjacent sequences:  A069787 A069788 A069789 * A069791 A069792 A069793

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 22:01 EST 2018. Contains 317116 sequences. (Running on oeis4.)