A068898 -id:A068898 - cp's OEIS frontend

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

Amarnath Murthy, Mar 21 2002

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

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

Cf. A020338, A068898.

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

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

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

A068897 Squares containing 2k digits in which the sum of the first k digits = that of the rest.

Original entry on oeis.org

5041, 108900, 122500, 128164, 137641, 155236, 173056, 185761, 203401, 206116, 216225, 287296, 288369, 302500, 324900, 342225, 368449, 423801, 434281, 459684, 485809, 515524, 531441, 540225, 675684, 698896, 720801, 737881, 749956, 779689

Offset: 1

Amarnath Murthy, Mar 21 2002

			5041 is a member with 5+0 = 4+1.

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Intersection of A000290 and A240927.

Cf. A068896, A068898.

isok(n)={my(d=digits(n)); my(k=#d); k%2==0 && vecsum(d[1..k/2]) == vecsum(d[k/2+1..k])}
lista(n)={my(L=List(), k=0); while(#LAndrew Howroyd, Sep 19 2024

Corrected and extended by Harvey P. Dale, Mar 31 2002

Offset changed by Andrew Howroyd, Sep 19 2024

cp's OEIS Frontend

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

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