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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
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
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
Sequence in context: A168109 A116055 A068898 * A053719 A217236 A050781
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