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

1, 13, 177, 1777, 15173, 135173, 3397973, 13535137, 135157537, 1193111377, 11979759377, 119595919137, 1195991117973, 11979931335173, 119777591993777, 1199999593111377, 11977793913551137, 119593573333335733, 1195935733333335733, 11977593393931151137, 119759371717733717537

Offset: 1

Author

M. F. Hasler, Nov 23 2021

Keywords

• nonn
• base

Comments

It appears that all a(n), n > 9, have initial digits "119".

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?

Links

• S. S. Gupta, Can You Find (CYF) no. 55, Nov 11 2021.
• A. Zimmermann, Al Zimmermann's Programming Contests: Oddly Triangular, Sep. 7-8, 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), A355277 (largest such k-digit term).

Programs

PARI

apply( A349247(n)=A347475_next(10^n\9), [1..15]) \\ Edited (moved function body to A347475) by M. F. Hasler, Sep 13 2022

Python

from itertools import product
def A349247(n):
    for a in product('13579',repeat=n):
        if set(str((m:=int(''.join(a)))*(m+1)>>1)) <= {'1', '3', '5', '7', '9'}:
            return m # Chai Wah Wu, Sep 08 2022

Python

A349247 = lambda n: next_A347475(10**n//9) # M. F. Hasler, Sep 10 2022

Formula

a(n) = min { k in A347475 | k >= 10^(n-1) }.