A257631 Near-repunit triangular numbers.

10, 15, 21, 91, 171, 1711

Offset: 1

Author

Shyam Sunder Gupta, Jul 12 2015

Keywords

• base
• nonn
• more

Comments

A near-repunit number is a number all but one of whose digits are 1's. No other near-repunit triangular number is known up to 10^15.

No more terms less than 10^1000. It is likely there are no more terms. - Chai Wah Wu, Mar 25 2020

Crossrefs

Cf. A000217, A002275, A062690, A257630.

Programs

Python

from sympy import integer_nthroot
def istri(n): return integer_nthroot(8*n+1, 2)[1]
def near_repunits(digits):
    for loc in range(1, digits):
        yield int("1"*loc + "0" + "1"*(digits-loc-1))
    for loc in range(1, digits+1):
        for d in "23456789":
            yield int("1"*(digits-loc) + d + "1"*(loc-1))
def afind(maxdigits):
    for digits in range(2, maxdigits+1):
        for t in near_repunits(digits):
            if istri(t): print(t, end=", ")
afind(200) # Michael S. Branicky, Oct 15 2021