A352148 Integers m such that nonzero digits of A000217(m) are all the same.
0, 1, 2, 3, 4, 10, 11, 24, 36, 44, 77, 100, 141, 363, 1000, 1095, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000
Offset: 1
Programs
-
Mathematica
(Sqrt[8 # + 1] - 1)/2 & /@ Sort[Select[ Flatten[Outer[Times, Table[FromDigits[IntegerDigits[n, 2]], {n, 2^22 - 1}], Range[9]]], IntegerQ[Sqrt[8 # + 1]] &]] -
PARI
isok(m) = #Set(select(x->(x>0), digits(m*(m+1)/2))) <= 1; \\ Michel Marcus, Mar 06 2022
-
Python
from itertools import count, islice from sympy import integer_nthroot def A352148_gen(): # generator of terms yield 0 for l in count(0): for d in range(1,10): for m in range(2**l,2**(l+1)): a, b = integer_nthroot(8*d*int(bin(m)[2:])+1,2) if b: yield (a-1)//2 A352148_list = list(islice(A352148_gen(),10)) # Chai Wah Wu, Apr 08 2022
Formula
Conjecture: a(n) = 10^(n-13) for n >= 17.
Extensions
a(25)-a(27) from Chai Wah Wu, Apr 08 2022
a(28)-a(29) from Chai Wah Wu, Apr 09 2022