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

5, 17, 177, 5573, 79137, 791377, 7913777, 79971937, 557335733, 5995957537, 59995599137, 599591791137, 7991739957973, 79971739957537, 799739357539937, 7991713197753777, 79991971791119137, 799999173991317537, 7997391313911797973

Offset: 1

Author

M. F. Hasler, Sep 07 2022

Keywords

• nonn
• base

Comments

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

The first digit of a(n) is never 9. - Chai Wah Wu, Sep 08 2022

As in A347475, all terms with more than 2 digits end in 33, 37, 73 or 77. - M. F. Hasler, Sep 12 2022

Examples

			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.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..24, Sep 08 2022
• S. S. Gupta, Can You Find (CYF) no. 55, Nov 11 2021.

Crossrefs

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).

Programs

PARI

apply( A355277(n)=A347475_prec(10^n), [1..15]) \\ M. F. Hasler, Sep 08 2022

Python

from itertools import product
def A355277(n):
    for a in '7531':
        for b in product('97531',repeat=n-1):
            m = int(a+''.join(b))
            if set(str(m*(m+1)>>1)) <= {'1', '3', '5', '7', '9'}:
                return m # Chai Wah Wu, Sep 08 2022

Formula

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