A257631 - OEIS

%I #30 Oct 15 2021 06:06:04

%S 10,15,21,91,171,1711

%N Near-repunit triangular numbers.

%C 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.

%C No more terms less than 10^1000. It is likely there are no more terms. - _Chai Wah Wu_, Mar 25 2020

%o (Python)

%o from sympy import integer_nthroot

%o def istri(n): return integer_nthroot(8*n+1, 2)[1]

%o def near_repunits(digits):

%o     for loc in range(1, digits):

%o         yield int("1"*loc + "0" + "1"*(digits-loc-1))

%o     for loc in range(1, digits+1):

%o         for d in "23456789":

%o             yield int("1"*(digits-loc) + d + "1"*(loc-1))

%o def afind(maxdigits):

%o     for digits in range(2, maxdigits+1):

%o         for t in near_repunits(digits):

%o             if istri(t): print(t, end=", ")

%o afind(200) # _Michael S. Branicky_, Oct 15 2021

%Y Cf. A000217, A002275, A062690, A257630.

%K base,nonn,more

%O 1,1

%A _Shyam Sunder Gupta_, Jul 12 2015