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A355277 Largest n-digit number k with only odd digits such that the k-th triangular number also has only odd digits.

%I A355277 #27 Sep 15 2022 11:47:40
%S A355277 5,17,177,5573,79137,791377,7913777,79971937,557335733,5995957537,
%T A355277 59995599137,599591791137,7991739957973,79971739957537,
%U A355277 799739357539937,7991713197753777,79991971791119137,799999173991317537,7997391313911797973
%N A355277 Largest n-digit number k with only odd digits such that the k-th triangular number also has only odd digits.
%C A355277 It appears that all a(n), n > 12, have initial digits "799".
%C A355277 The first digit of a(n) is never 9. - _Chai Wah Wu_, Sep 08 2022
%C A355277 As in A347475, all terms with more than 2 digits end in 33, 37, 73 or 77. - _M. F. Hasler_, Sep 12 2022
%H A355277 M. F. Hasler, <a href="/A355277/b355277.txt">Table of n, a(n) for n = 1..24</a>, Sep 08 2022
%H A355277 S. S. Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can You Find (CYF) no. 55</a>, Nov 11 2021.
%F A355277 a(n) = max { k in A347475 | k < 10^n }.
%e A355277 T(5) = A000217(5) = 5*6/2 = 5*3 = 15 has only odd digits, and neither T(7) nor T(9) have this property, therefore a(1) = 5.
%o A355277 (Python)
%o A355277 from itertools import product
%o A355277 def A355277(n):
%o A355277     for a in '7531':
%o A355277         for b in product('97531',repeat=n-1):
%o A355277             m = int(a+''.join(b))
%o A355277             if set(str(m*(m+1)>>1)) <= {'1', '3', '5', '7', '9'}:
%o A355277                 return m # _Chai Wah Wu_, Sep 08 2022
%o A355277 (PARI) apply( A355277(n)=A347475_prec(10^n), [1..15]) \\ _M. F. Hasler_, Sep 08 2022
%Y A355277 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), A349247 (least k-digit term).
%K A355277 nonn,base
%O A355277 1,1
%A A355277 _M. F. Hasler_, Sep 07 2022