A007632 -id:A007632 - cp's OEIS frontend

A308311 Numbers n which are palindromic in base b, where b = sum of digits of n in base 10.

16, 39, 41, 55, 96, 104, 123, 130, 141, 142, 155, 170, 181, 187, 214, 239, 250, 251, 260, 262, 274, 341, 343, 365, 385, 418, 422, 424, 435, 443, 464, 471, 494, 503, 505, 507, 543, 562, 599, 632, 665, 685, 706, 708, 753, 754, 818, 823, 835, 838, 843, 850, 859

Offset: 1

Metin Sariyar, Sep 26 2019

			41 is a term because 41 = 131 in base 5 = 1 + 4.

Metin Sariyar, Table of n, a(n) for n = 1..10000
Caldwell and Honaker, Prime Curio for 41.

Cf. A007632.

Select[Range[10^5],#==IntegerReverse[#, Total[IntegerDigits[#]]]&]

isok(n) = my(s=sumdigits(n)); if (s> 1, my(d = digits(n, s)); d == Vecrev(d)); \\ Michel Marcus, Sep 26 2019

A340559 Numbers that are palindromic in base 2 and base 16.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 15, 17, 51, 85, 119, 153, 255, 257, 273, 771, 819, 1285, 1317, 1365, 1397, 1799, 1831, 1879, 1911, 2313, 2409, 2457, 2553, 3855, 3951, 3999, 4095, 4097, 4369, 12291, 13107, 20485, 21029, 21845, 22389, 28679, 29223, 30039, 30583, 36873, 38505

Offset: 1

Glen Gilchrist, Jan 11 2021

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Intersection of A006995 and A029730.

Cf. A029731, A007632.

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

A046472 Primes that are palindromic in bases 2 and 10.

Original entry on oeis.org

3, 5, 7, 313, 7284717174827, 390714505091666190505417093

Offset: 1

Patrick De Geest, Aug 15 1998

			313_10 = 100111001_2. - _Jon E. Schoenfield_, Apr 10 2021

P. De Geest, World!Of Palindromic Primes

Cf. A002385 (palindromic primes), A007632 (palindromes in bases 2 and 10).

Select[Prime[Range[10!]], IntegerDigits[#]==Reverse[IntegerDigits[#]] && IntegerDigits[#,2]==Reverse[IntegerDigits[#,2]]&] (* Vladimir Joseph Stephan Orlovsky, Dec 30 2010 *)
p = Sort[Reap[Do[d=IntegerDigits[n]; p1=FromDigits[Join[Most[d], Reverse[d]]]; p2=FromDigits[Join[d, Reverse[d]]]; If[IntegerDigits[p1, 2] == Reverse[IntegerDigits[p1, 2]], Sow[p1]]; If[IntegerDigits[p2, 2] == Reverse[IntegerDigits[p2, 2]], Sow[p2]], {n, 0, 9999999}]][[2, 1]]]; Select[p, PrimeQ]

a(6) (from A007632) added by T. D. Noe, Dec 31 2010

A124404 Nonpalindromes in base 10 that are non-palindromes in base 2.

Original entry on oeis.org

10, 12, 13, 14, 16, 18, 19, 20, 23, 24, 25, 26, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 67, 68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98

Offset: 1

Tanya Khovanova, Dec 26 2006

Cf. A007632 = numbers that are palindromic in bases 2 and 10.

Select[Range[100], Reverse[IntegerDigits[ # ]] != IntegerDigits[ # ] && Reverse[IntegerDigits[ #, 2]] != IntegerDigits[ #, 2] &]

A127916 Number of n-digit palindromes in bases 2 and 10. Also difference of A120764(n).

Original entry on oeis.org

6, 2, 3, 2, 6, 1, 7, 1, 3, 2, 4, 2, 10, 1, 2, 2, 7, 2, 2, 3, 2, 0, 4, 0, 6, 1, 6, 1, 5, 1, 2, 0, 3

Offset: 1

Anton Chupin (chupin(AT)icmm.ru), Apr 08 2007

			Palindromes in bases 2 and 10 are (A007632): 0, 1, 3, 5, 7, 9, 33, 99, 313, 585, 717, 7447, 9009, 15351, 32223... So a(1)=6 one-digit numbers, a(2)=2 two-digit palindromes and so on.

P. De Geest, Palindromic numbers beyond base 10
Charlton Harrison, Binary/Decimal Palindromes

Cf. A120764, A007632.

cp's OEIS Frontend

A308311 Numbers n which are palindromic in base b, where b = sum of digits of n in base 10.

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A340559 Numbers that are palindromic in base 2 and base 16.

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A046472 Primes that are palindromic in bases 2 and 10.

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A124404 Nonpalindromes in base 10 that are non-palindromes in base 2.

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A127916 Number of n-digit palindromes in bases 2 and 10. Also difference of A120764(n).

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