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A068899 Triangular numbers containing 2n digits obtained by duplicating the first n digits; i.e., triangular numbers in A020338. 5
55, 66, 5050, 5151, 203203, 255255, 426426, 500500, 501501, 581581, 828828, 930930, 39653965, 50005000, 50015001, 61566156, 3347133471, 5000050000, 5000150001, 6983669836, 220028220028, 500000500000, 500001500001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence is infinite: the 10^n-th and the (10^n + 1)-th triangular numbers are members. It is a subsequence of A068898.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 10: # to get all terms of up to 2N digits

Res:= NULL:

for n from 1 to N do

   Divs:= select(t -> igcd(t, (10^n+1)/t)=1, numtheory:-divisors(10^n+1));

   for d in Divs do

     for e in [1, 3] do

      u:= chrem([1, -1, e], [d, (10^n+1)/d, 4]);

      y:= (u^2-1)/8/(10^n+1);

      if y >= 10^(n-1) and y < 10^n then Res:= Res, y*(10^n+1) fi;

od od od:

sort([Res]); # Robert Israel, Feb 27 2017

CROSSREFS

Cf. A020338, A068898.

Sequence in context: A168109 A116055 A068898 * A053719 A217236 A050781

Adjacent sequences:  A068896 A068897 A068898 * A068900 A068901 A068902

KEYWORD

easy,nonn,base,look

AUTHOR

Amarnath Murthy, Mar 21 2002

EXTENSIONS

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jan 10 2003

STATUS

approved

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Last modified August 26 03:38 EDT 2019. Contains 326324 sequences. (Running on oeis4.)