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

1,2

Links

Table of n, a(n) for n=1..57.

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A188025 A187949 A180161 * A099261 A103215 A037942

Adjacent sequences: A349240 A349241 A349242 * A349244 A349245 A349246

Keyword

nonn,base

Author

M. F. Hasler, Nov 20 2021

Status

approved