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A352148
Integers m such that nonzero digits of A000217(m) are all the same.
1
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
1,3
FORMULA
Conjecture: a(n) = 10^(n-13) for n >= 17.
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]] &]]
PROG
(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
CROSSREFS
Cf. A000217, A352057 (resulting triangular numbers).
Sequence in context: A353243 A115897 A116019 * A259561 A087460 A082866
KEYWORD
nonn,base,more
AUTHOR
Steven Lu, Mar 06 2022
EXTENSIONS
a(25)-a(27) from Chai Wah Wu, Apr 08 2022
a(28)-a(29) from Chai Wah Wu, Apr 09 2022
STATUS
approved