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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.
4
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Sep 07 2022
STATUS
approved