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A349247 Least n-digit number k with only odd digits such that the k-th triangular number also has only odd digits.

%I A349247 #27 Sep 21 2022 17:54:42
%S A349247 1,13,177,1777,15173,135173,3397973,13535137,135157537,1193111377,
%T A349247 11979759377,119595919137,1195991117973,11979931335173,
%U A349247 119777591993777,1199999593111377,11977793913551137,119593573333335733,1195935733333335733,11977593393931151137,119759371717733717537
%N A349247 Least n-digit number k with only odd digits such that the k-th triangular number also has only odd digits.
%C A349247 It appears that all a(n), n > 9, have initial digits "119".
%C A349247 It also appears that the sequence of digits of the terms converges to a limit, (1, 1, 9, 3, 1, ...). Can this be proved or disproved?
%H A349247 S. S. Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can You Find (CYF) no. 55</a>, Nov 11 2021.
%H A349247 A. Zimmermann, <a href="http://azspcs.com/Contest/OddlyTriangular">Al Zimmermann's Programming Contests: Oddly Triangular</a>, Sep. 7-8, 2022
%F A349247 a(n) = min { k in A347475 | k >= 10^(n-1) }.
%o A349247 (PARI) apply( A349247(n)=A347475_next(10^n\9), [1..15]) \\ Edited (moved function body to A347475) by _M. F. Hasler_, Sep 13 2022
%o A349247 (Python)
%o A349247 from itertools import product
%o A349247 def A349247(n):
%o A349247     for a in product('13579',repeat=n):
%o A349247         if set(str((m:=int(''.join(a)))*(m+1)>>1)) <= {'1', '3', '5', '7', '9'}:
%o A349247             return m # _Chai Wah Wu_, Sep 08 2022
%o A349247 (Python) A349247 = lambda n: next_A347475(10**n//9) # _M. F. Hasler_, Sep 10 2022
%Y A349247 Cf. A000217 (triangular numbers), A014261 (numbers with only odd digits), A117960 (triangular numbers with only odd digits), A349243 (indices of the former), A347475 (such indices with only odd digits), A355277 (largest such k-digit term).
%K A349247 nonn,base
%O A349247 1,2
%A A349247 _M. F. Hasler_, Nov 23 2021