A355277 - OEIS

%I #27 Sep 15 2022 11:47:40

%S 5,17,177,5573,79137,791377,7913777,79971937,557335733,5995957537,

%T 59995599137,599591791137,7991739957973,79971739957537,

%U 799739357539937,7991713197753777,79991971791119137,799999173991317537,7997391313911797973

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

%C It appears that all a(n), n > 12, have initial digits "799".

%C The first digit of a(n) is never 9. - _Chai Wah Wu_, Sep 08 2022

%C As in A347475, all terms with more than 2 digits end in 33, 37, 73 or 77. - _M. F. Hasler_, Sep 12 2022

%H M. F. Hasler, <a href="/A355277/b355277.txt">Table of n, a(n) for n = 1..24</a>, Sep 08 2022

%H S. S. Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can You Find (CYF) no. 55</a>, Nov 11 2021.

%F a(n) = max { k in A347475 | k < 10^n }.

%e 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 (Python)

%o from itertools import product

%o def A355277(n):

%o     for a in '7531':

%o         for b in product('97531',repeat=n-1):

%o             m = int(a+''.join(b))

%o             if set(str(m*(m+1)>>1)) <= {'1', '3', '5', '7', '9'}:

%o                 return m # _Chai Wah Wu_, Sep 08 2022

%o (PARI) apply( A355277(n)=A347475_prec(10^n), [1..15]) \\ _M. F. Hasler_, Sep 08 2022

%Y 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 nonn,base

%O 1,1

%A _M. F. Hasler_, Sep 07 2022