A068899 Triangular numbers containing 2n digits obtained by duplicating the first n digits; i.e., triangular numbers in A020338.

55, 66, 5050, 5151, 203203, 255255, 426426, 500500, 501501, 581581, 828828, 930930, 39653965, 50005000, 50015001, 61566156, 3347133471, 5000050000, 5000150001, 6983669836, 220028220028, 500000500000, 500001500001

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

Mathematica

Select[Accumulate[Range[5*10^6]], EvenQ[IntegerLength[#]]&&Take[ IntegerDigits[ #], IntegerLength[ #]/2]== Take[IntegerDigits[#], -IntegerLength[#]/2]&] (* Harvey P. Dale, Aug 20 2022 *)

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