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.
is(n,b=16,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)
a(17) = 17 because 17 in hexadecimal is 11, the same as its reverse. a(18) = 33 because 18 in hexadecimal is 12, and hexadecimal 21 is 2 * 16 + 1 = 33. a(19) = 49 because 19 in hexadecimal is 13, and hexadecimal 31 is 3 * 16 + 1 = 49.
Table[FromDigits[Reverse[IntegerDigits[n, 16]], 16], {n, 0, 127}] (* Alonso del Arte, Sep 30 2018 *)
a(n) = fromdigits(Vecrev(digits(n, 16)), 16); \\ Michel Marcus, Sep 30 2018
674 in base-16: 2,10,2 having DV = 8, UV = 8, so that 674 is in the sequence.
g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
b = 16; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
Take[Flatten[Position[w, -1]], 120] (* A297288 *)
Take[Flatten[Position[w, 0]], 120] (* A297289 *)
Take[Flatten[Position[w, 1]], 120] (* A297290 *)
4095 = 111111111111_2 = 333333_4 = 7777_8 = FFF_16. Hence 4095 is in the sequence.
palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && palQ[n, 4] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
[n for n in (0..100000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(4)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
255 is 11111111 in binary, 3333 in quaternary and FF in hexadecimal. Hence 255 is in the sequence. Although 21 is 10101 in binary and 111 in quaternary, it is 15 in hexadecimal and therefore not in the sequence.
[n: n in [0..2*10^7] | Intseq(n, 2) eq Reverse(Intseq(n, 2)) and Intseq(n, 4) eq Reverse(Intseq(n, 4)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
extend:= proc(x, d)
local a,b,m;
if d::odd then
m:= (d-1)/2;
a:= x mod 16^(m+1);
b:= floor(x/16^m);
a + 16^(m+1)*b
else
m:= d/2;
a:= x mod 16^m;
b:= floor(x/16^m);
(a + 16^(m+1)*b, a + 16^m * (a mod 16) + 16^(m+1)*b)
fi
end proc:
V:= [1,3,5,15]: R:= 0, op(V):
for d from 1 to 6 do
V:= map(extend,V,d);
R:= R, op(V);
od:
R; # Robert Israel, Nov 12 2023
palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && palQ[n, 4] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
[n for n in (0..1000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(4)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
Select[Range[0, 10^5], PalindromeQ @ IntegerDigits[#, 2] && PalindromeQ @ IntegerDigits[#, 16] &] (* Amiram Eldar, Jan 11 2021 *)
ispal(m, b) = my(d=digits(m, b)); d == Vecrev(d); isok(m) = ispal(m, 2) && ispal(m, 16); \\ Michel Marcus, Jan 20 2021
def palindrome(x):
res = str(x) == str(x)[::-1]
return res
def dec_to_bin(x):
return int(bin(x)[2:])
def dec_to_hex(x):
return (hex(x)[2:])
for x in range (1,10000):
if palindrome(dec_to_hex(x)) & palindrome(dec_to_bin(x)) == True:
print(x)
(BASIC:- MM Basic, a modern QBASIC variant, https://www.mmbasic.com/)
Function reverse(in_string$) As string
Local r$
Local i
For i = Len(in_string$) To 1 Step -1
b$=Mid$(in_string$,i,1)
r$=r$+b$
Next i
reverse=r$
End Function
For i = 1 To 10000
If Bin$(i) = reverse(Bin$(i)) Then
If Hex$(i) = reverse(Hex$(i)) Then
Print i,Bin$(i), Hex$(i)
EndIf
EndIf
Next i
16187247 = 111101101111111101101111_2 = 75577557_8 = F6FF6F_16.
[n: n in [0..2*10^7] | Intseq(n, 2) eq Reverse(Intseq(n, 2)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
[n for n in (0..10000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
170 = 2222_4 = 252_8 = AA_16. Hence 170 is in the sequence.
[n: n in [0..2*10^7] | Intseq(n, 4) eq Reverse(Intseq(n, 4)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 4] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
[n for n in (0..100000) if Word(n.digits(4)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
Comments