A349243 Indices of triangular numbers A000217 with only odd digits.

1, 2, 5, 10, 13, 17, 18, 26, 34, 58, 62, 101, 109, 138, 149, 154, 177, 178, 186, 189, 250, 257, 266, 382, 554, 586, 589, 621, 622, 862, 893, 1013, 1050, 1057, 1069, 1258, 1354, 1370, 1634, 1658, 1738, 1754, 1777, 1786, 1853, 1885, 1965, 2657, 2666, 2741, 2818, 3218, 3346, 3445, 3457, 3794, 3845

Offset: 1

Author

M. F. Hasler, Nov 20 2021

Keywords

• nonn
• base

Links

• S. S. Gupta, Can You Find (CYF) no. 55, Nov 11 2021.

Crossrefs

Cf. A000217 (triangular numbers), A014261 (numbers with only odd digits), A117960 (triangular numbers with only odd digits).

Programs

Maple

a:= proc(n) option remember; local k; for k from
      1+`if`(n=1, 0, b(n-1)) while 0=mul(irem(i, 2),
      i=convert(k*(k+1)/2, base, 10)) do od; k
    end:
seq(a(n), n=1..57);  # Alois P. Heinz, Nov 22 2021

Mathematica

Select[Range[4000], AllTrue[IntegerDigits[#*(# + 1)/2], OddQ] &] (* Amiram Eldar, Nov 20 2021 *)
Position[Accumulate[Range[4000]],?(AllTrue[IntegerDigits[#],OddQ]&)]//Flatten (* _Harvey P. Dale, Sep 06 2023 *)

PARI

select( {is_A349243(n)=Set(digits(n*(n+1)\2)%2)==[1]}, [1..9999])

Python

from itertools import islice, count
def A349243(): return filter(lambda n: set(str(n*(n+1)//2)) <= {'1','3','5','7','9'}, count(0))
A349243_list = list(islice(A349243(),20)) # Chai Wah Wu, Nov 22 2021

Formula

a(n) = floor(sqrt(2*A117960(n))).