This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Joonas Pohjonen has authored 7 sequences.
a(2) = 43 since 43 has two distinct digits in bases 2 <= b <= 5, 7 <= b <= 41 and b = 43, and one distinct digit in bases b = 6, b = 42 and b >= 44. All greater numbers have at least 3 distinct digits in some base b >= 2.
a(5) = 67 = 232_5, since all its substrings in base 5 (2, 3, 23_5 = 13, 32_5 = 17 and 232_5 = 67) are primes. There are no greater primes with this property.
See Links section.
16 = 121_3, replacing 2 with 0 gives 101_3 = 10, so a(16) = 10.
a:= proc(n) local t, r, i; t, r:= n, 0;
for i from 0 while t>0 do
r:= r+3^i*(d-> `if`(d=2, 0, d))(irem(t, 3, 't'))
od; r
end:
seq(a(n), n=0..80); # Alois P. Heinz, Jun 17 2014
Array[FromDigits[IntegerDigits[#, 3] /. 2 -> 0, 3] &, 72, 0] (* Michael De Vlieger, Mar 17 2018 *)
a(n) = my(d=digits(n, 3)); fromdigits(apply(x->(if (x==2, 0, x)), d), 3); \\ Michel Marcus, Jun 10 2017
from sympy.ntheory.factor_ import digits
def a(n):return int("".join(map(str, digits(n, 3)[1:])).replace('2', '0'), 3) # Indranil Ghosh, Jun 10 2017
import Data.List (unfoldr, nub); import Data.Tuple (swap)
a235708 n = f n where
f 1 = 1
f b = if isPandigital b n then b else f (b - 1) where
isPandigital b = (== b) . length . nub . unfoldr
(\x -> if x == 0 then Nothing else Just $ swap $ divMod x b)
-- Reinhard Zumkeller, May 12 2014
11 is not in the sequence because 11 = 102_3.
nop[n_] := Block[{b=3, d}, While[ Length[d = IntegerDigits[n, b]] >= b && Union[d] != Range[0, b-1], b++]; Length[d] < b]; Select[Range[0, 124], nop] (* Giovanni Resta, Mar 17 2014 *)
isok(n) = {for (b = 3, n, d = digits(n, b); if (#vecsort(d,,8) == b, return(0));); return (1);} \\ Michel Marcus, Mar 17 2014
is(n)=for(b=3,log(n)\lambertw(log(n))+1, if(#Set(digits(n,b))==b, return(0))); 1 \\ Charles R Greathouse IV, Mar 17 2014
Prepend[Cases[Range[329], n_ /; NoneTrue[Range[2, (Sqrt[4 n - 3] - 1)/2], MatchQ[IntegerDigits[n, #], {_, d_, d_, d_, _}] &]], 0] (* Vladimir Reshetnikov, Mar 20 2022 *)
from sympy.ntheory.digits import digits
def three_in_a_row(s):
return any(s[i] == s[i+1] == s[i+2] for i in range(len(s) - 2))
def ok(n):
if n < 7: return True
b = 2
d = digits(n, b)[1:]
while len(d) >= 3:
if three_in_a_row(d): return False
b += 1
d = digits(n, b)[1:]
return True
print([k for k in range(331) if ok(k)]) # Michael S. Branicky, Mar 27 2022
SortBy[Table[{n,Total[N[Sqrt[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]]]},{n,150}],Last][[;;,1]] (* Harvey P. Dale, May 20 2023 *)
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