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A349243 Indices of triangular numbers A000217 with only odd digits.

%I A349243 #21 Sep 06 2023 13:25:00
%S A349243 1,2,5,10,13,17,18,26,34,58,62,101,109,138,149,154,177,178,186,189,
%T A349243 250,257,266,382,554,586,589,621,622,862,893,1013,1050,1057,1069,1258,
%U A349243 1354,1370,1634,1658,1738,1754,1777,1786,1853,1885,1965,2657,2666,2741,2818,3218,3346,3445,3457,3794,3845
%N A349243 Indices of triangular numbers A000217 with only odd digits.
%H A349243 S. S. Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can You Find (CYF) no. 55</a>, Nov 11 2021.
%F A349243 a(n) = floor(sqrt(2*A117960(n))).
%p A349243 a:= proc(n) option remember; local k; for k from
%p A349243       1+`if`(n=1, 0, b(n-1)) while 0=mul(irem(i, 2),
%p A349243       i=convert(k*(k+1)/2, base, 10)) do od; k
%p A349243     end:
%p A349243 seq(a(n), n=1..57);  # _Alois P. Heinz_, Nov 22 2021
%t A349243 Select[Range[4000], AllTrue[IntegerDigits[#*(# + 1)/2], OddQ] &] (* _Amiram Eldar_, Nov 20 2021 *)
%t A349243 Position[Accumulate[Range[4000]],_?(AllTrue[IntegerDigits[#],OddQ]&)]//Flatten (* _Harvey P. Dale_, Sep 06 2023 *)
%o A349243 (PARI) select( {is_A349243(n)=Set(digits(n*(n+1)\2)%2)==[1]}, [1..9999])
%o A349243 (Python)
%o A349243 from itertools import islice, count
%o A349243 def A349243(): return filter(lambda n: set(str(n*(n+1)//2)) <= {'1','3','5','7','9'}, count(0))
%o A349243 A349243_list = list(islice(A349243(),20)) # _Chai Wah Wu_, Nov 22 2021
%Y A349243 Cf. A000217 (triangular numbers), A014261 (numbers with only odd digits), A117960 (triangular numbers with only odd digits).
%K A349243 nonn,base
%O A349243 1,2
%A A349243 _M. F. Hasler_, Nov 20 2021