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

%I A068899 #12 Aug 20 2022 17:17:03
%S A068899 55,66,5050,5151,203203,255255,426426,500500,501501,581581,828828,
%T A068899 930930,39653965,50005000,50015001,61566156,3347133471,5000050000,
%U A068899 5000150001,6983669836,220028220028,500000500000,500001500001
%N A068899 Triangular numbers containing 2n digits obtained by duplicating the first n digits; i.e., triangular numbers in A020338.
%C A068899 The sequence is infinite: the 10^n-th and the (10^n + 1)-th triangular numbers are members. It is a subsequence of A068898.
%H A068899 Robert Israel, <a href="/A068899/b068899.txt">Table of n, a(n) for n = 1..10000</a>
%p A068899 N:= 10: # to get all terms of up to 2N digits
%p A068899 Res:= NULL:
%p A068899 for n from 1 to N do
%p A068899    Divs:= select(t -> igcd(t,(10^n+1)/t)=1, numtheory:-divisors(10^n+1));
%p A068899    for d in Divs do
%p A068899      for e in [1,3] do
%p A068899       u:= chrem([1,-1,e],[d,(10^n+1)/d,4]);
%p A068899       y:= (u^2-1)/8/(10^n+1);
%p A068899       if y >= 10^(n-1) and y < 10^n then Res:= Res, y*(10^n+1) fi;
%p A068899 od od od:
%p A068899 sort([Res]); # _Robert Israel_, Feb 27 2017
%t A068899 Select[Accumulate[Range[5*10^6]],EvenQ[IntegerLength[#]]&&Take[ IntegerDigits[ #],IntegerLength[ #]/2]== Take[IntegerDigits[#],-IntegerLength[#]/2]&] (* _Harvey P. Dale_, Aug 20 2022 *)
%Y A068899 Cf. A020338, A068898.
%K A068899 easy,nonn,base,look
%O A068899 1,1
%A A068899 _Amarnath Murthy_, Mar 21 2002
%E A068899 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jan 10 2003