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

1,1

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

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.

Formula

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

Example

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.

Prog

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

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).

Sequence in context: A182066 A090886 A097490 * A309178 A164740 A053678

Adjacent sequences: A355274 A355275 A355276 * A355278 A355279 A355280

Keyword

nonn,base

Author

M. F. Hasler, Sep 07 2022

Status

approved