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A068899 Triangular numbers containing 2n digits obtained by duplicating the first n digits; i.e., triangular numbers in A020338. 5

%I

%S 55,66,5050,5151,203203,255255,426426,500500,501501,581581,828828,

%T 930930,39653965,50005000,50015001,61566156,3347133471,5000050000,

%U 5000150001,6983669836,220028220028,500000500000,500001500001

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

%C 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 Robert Israel, <a href="/A068899/b068899.txt">Table of n, a(n) for n = 1..10000</a>

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

%p Res:= NULL:

%p for n from 1 to N do

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

%p for d in Divs do

%p for e in [1,3] do

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

%p y:= (u^2-1)/8/(10^n+1);

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

%p od od od:

%p sort([Res]); # _Robert Israel_, Feb 27 2017

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

%Y Cf. A020338, A068898.

%K easy,nonn,base,look

%O 1,1

%A _Amarnath Murthy_, Mar 21 2002

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

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Last modified October 5 23:01 EDT 2022. Contains 357261 sequences. (Running on oeis4.)