A345348 Triangular numbers that in base 2 have the same number of 0's and 1's.

10, 153, 210, 595, 666, 820, 2278, 2701, 9045, 9870, 10585, 11476, 12403, 13366, 13861, 14365, 34191, 34716, 35245, 36046, 37675, 37950, 39340, 39621, 40470, 41905, 42195, 42778, 43365, 44551, 45150, 45451, 46665, 48516, 49455, 50086, 50403, 51681, 52003, 52326

Offset: 1

Author

Ctibor O. Zizka, Jun 15 2021

Keywords

• nonn
• base

Examples

			Triangular number 153 = '10011001' in binary, the number of 1's equals the number of 0's, so 153 is a term.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000217 and A031443.

Cf. A164343.

Programs

Mathematica

Select[Table[n*(n + 1)/2, {n, 0, 330}], Equal @@ DigitCount[#, 2] &] (* Amiram Eldar, Jun 15 2021 *)

PARI

isA031443(n)=2*hammingweight(n)==exponent(n)+1
list(lim)=my(v=List(),n=4,t); while((t=n*n++/2)<=lim, if(isA031443(t), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Jun 21 2021

Python

A345348_list = [n for n in (m*(m+1)//2 for m in range(10**6)) if len(bin(n))-2 == 2*bin(n).count('1')] # Chai Wah Wu, Jun 21 2021

Extensions

More terms from Jinyuan Wang, Jun 15 2021