cp's OEIS Frontend

A352148 Integers m such that nonzero digits of A000217(m) are all the same.

%I A352148 #33 Apr 09 2022 11:10:25
%S A352148 0,1,2,3,4,10,11,24,36,44,77,100,141,363,1000,1095,10000,100000,
%T A352148 1000000,10000000,100000000,1000000000,10000000000,100000000000,
%U A352148 1000000000000,10000000000000,100000000000000,1000000000000000,10000000000000000
%N A352148 Integers m such that nonzero digits of A000217(m) are all the same.
%F A352148 Conjecture: a(n) = 10^(n-13) for n >= 17.
%t A352148 (Sqrt[8 # + 1] - 1)/2 & /@
%t A352148 Sort[Select[
%t A352148    Flatten[Outer[Times,
%t A352148      Table[FromDigits[IntegerDigits[n, 2]], {n, 2^22 - 1}],
%t A352148      Range[9]]], IntegerQ[Sqrt[8 # + 1]] &]]
%o A352148 (PARI) isok(m) = #Set(select(x->(x>0), digits(m*(m+1)/2))) <= 1; \\ _Michel Marcus_, Mar 06 2022
%o A352148 (Python)
%o A352148 from itertools import count, islice
%o A352148 from sympy import integer_nthroot
%o A352148 def A352148_gen(): # generator of terms
%o A352148     yield 0
%o A352148     for l in count(0):
%o A352148         for d in range(1,10):
%o A352148             for m in range(2**l,2**(l+1)):
%o A352148                 a, b = integer_nthroot(8*d*int(bin(m)[2:])+1,2)
%o A352148                 if b:
%o A352148                     yield (a-1)//2
%o A352148 A352148_list = list(islice(A352148_gen(),10)) # _Chai Wah Wu_, Apr 08 2022
%Y A352148 Cf. A000217, A352057 (resulting triangular numbers).
%K A352148 nonn,base,more
%O A352148 1,3
%A A352148 _Steven Lu_, Mar 06 2022
%E A352148 a(25)-a(27) from _Chai Wah Wu_, Apr 08 2022
%E A352148 a(28)-a(29) from _Chai Wah Wu_, Apr 09 2022