cp's OEIS Frontend

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.

Previous Showing 31-36 of 36 results.

A259383 Palindromic numbers in bases 5 and 8 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 18, 36, 186, 438, 2268, 2709, 11898, 18076, 151596, 228222, 563786, 5359842, 32285433, 257161401, 551366532, 621319212, 716064597, 2459962002, 5018349804, 5067084204, 7300948726, 42360367356, 139853034114, 176616961826, 469606524278, 669367713609, 1274936571666, 1284108810066, 5809320306961, 8866678870082, 11073162740322, 14952142559323, 325005646077513
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			186 is in the sequence because 186_10 = 272_8 = 1221_5.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 5], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=5; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A029952 and A029803.

A259387 Palindromic numbers in bases 4 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 255, 273, 373, 546, 2550, 2730, 2910, 16319, 23205, 54215, 1181729, 1898445, 2576758, 3027758, 3080174, 4210945, 9971750, 163490790, 2299011170, 6852736153, 6899910553, 160142137430, 174913133450, 204283593150, 902465909895, 1014966912315, 2292918574418, 9295288254930, 11356994802010, 11372760382810, 38244097345762
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			273 is in the sequence because 273_10 = 333_9 = 10101_4.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=9; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A014192 and A029955.

A259388 Palindromic numbers in bases 5 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 109, 246, 282, 564, 701, 22386, 32152, 41667, 47653, 48553, 1142597, 1313858, 1412768, 1677684, 12607012902, 19671459008, 20134447808, 24208576998, 24863844904, 26358878059
Offset: 1

Views

Author

Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			246 is in the sequence because 246_10 = 303_9 = 1441_5.

Links

Crossrefs

Cf. A007632, A007633, A029731, A029804, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A048268, A060792, A097855, A097856, A097928, A097929, A097930, A097931, A099145, A099146, A099165, A182232, A182233, A182234, A250408, A250409, A250410, A250411, A250412, A259374, A259375, A259376, A259377, A259378, A249156, A259380, A259381, A259382, A259383, A259384, A259385, A259386, A259387, A259388, A259389, A259390.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 5], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=5; b2=9; lst={};Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A029952 and A029955.

A259389 Palindromic numbers in bases 6 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 80, 154, 191, 209, 910, 3740, 5740, 8281, 16562, 16814, 2295481, 2300665, 2350165, 2439445, 2488945, 2494129, 2515513, 7971580, 48307924, 61281793, 69432517, 123427622, 124091822, 124443290, 55854298990, 184314116750, 185794441250, 187195815770, 327925630018, 7264479038060, 27832011695551
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 17 2015

Keywords

Examples

			209 is in the sequence because 209_10 = 252_9 = 545_6.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 6], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=6; b2=9; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 1000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A029953 and A029955.

A248889 Palindromic in base 10 and 18.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 171, 323, 343, 505, 595, 686, 848, 1661, 2112, 3773, 23332, 46664, 69996, 262262, 583385, 782287, 859958, 981189, 1254521, 1403041, 1832381, 39388393, 54411445, 55499455, 88844888, 118919811, 191010191
Offset: 1

Views

Author

Mauro Fiorentini, Mar 05 2015

Keywords

Comments

a(54) > 10^12.

Examples

			848 in decimal is 2B2 in base 18, so 848 is in the sequence.
1661 in decimal is 525 in base 18, so 1661 is in the sequence.
1771 in decimal is 587 in base 18, which is not a palindrome, so 1771 is not in the sequence.

Links

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A028731, A097855, A248899

Programs

  • Magma
    [n: n in [0..2*10^7] | Intseq(n) eq Reverse(Intseq(n)) and Intseq(n,18) eq Reverse(Intseq(n,18))]; // Vincenzo Librandi, Mar 21 2015
  • Maple
    IsPalindromic := proc(n, Base)
    local Conv, i;
    Conv := convert(n, base, Base);
    for i from 1 to nops(Conv) / 2 do
        if Conv [i] <> Conv [nops(Conv) + 1 - i] then
            return false;
        fi:
    od:
    true;
end proc:
Base := 18;
A := [];
for i from 1 to 10^6 do:
   S := convert(i, base, 10);
   V := 0;
   if i mod 10 = 0 then
      next;
   fi;
   for j from 1 to nops(S) do:
      V := V * 10 + S [j];
   od:
   for j from 0 to 10 do:
      V1 := V * 10^(nops(S) + j) + i;
      if IsPalindromic(V1, Base) then
         A := [op(A), V1];
      fi;
   od:
   V1 := (V - (V mod 10)) * 10^(nops(S) - 1) + i;
   if IsPalindromic(V1, Base) then
      A := [op(A), V1];
   fi;
od:
sort(A);
  • Mathematica
    palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[0, 499], palindromicQ[#] && palindromicQ[#, 18] &] (* Alonso del Arte, Mar 21 2015 *)
  • PARI
    isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 18)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 14 2015
  • Python
    def palgen10(l): # generator of palindromes of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1,l+1):
            n = 10**(x-1)
            n2 = n*10
            for y in range(n,n2):
                s = str(y)
                yield int(s+s[-2::-1])
            for y in range(n,n2):
                s = str(y)
                yield int(s+s[::-1])
def palcheck(n, b): # check if n is a palindrome in base b
    s = digits(n, b)
    return s == s[::-1]
A248889_list = [n for n in palgen10(9) if palcheck(n, 18)]
# Chai Wah Wu, Mar 23 2015

A248899 Numbers that are palindromic in bases 10 and 19.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 666, 838, 1771, 432234, 864468, 1551551, 1897981, 2211122, 155292551, 330050033, 453848354, 467535764, 650767056, 666909666, 857383758, 863828368, 47069796074, 62558085526, 67269596276, 87161116178, 96060106069, 121791197121, 127673376721, 139103301931, 234595595432, 246025520642
Offset: 1

Views

Author

Mauro Fiorentini, Mar 06 2015

Keywords

Comments

Next term > 10^12.

Examples

			838 = 262 in base 19.

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A248889.

Programs

  • Magma
    [n: n in [0..2*10^7] | Intseq(n) eq Reverse(Intseq(n))and Intseq(n, 19) eq Reverse(Intseq(n, 19))]; // Vincenzo Librandi, Mar 08 2015
  • Maple
    IsPalindromic := proc(n, Base)   local Conv, i;
   Conv := convert(n, base, Base);
for i from 1 to nops(Conv) / 2 do:
    if Conv [i] <> Conv [nops(Conv) + 1 - i] then
       return false:
    fi:
od:
return true;
end proc;
Base := 19;
A := [];
for i from 1 to 10^6 do:
   S := convert(i, base, 10);
   V := 0;
   if i mod 10 = 0 then
      next;
   fi;
   for j from 1 to nops(S) do:
      V := V * 10 + S [j];
   od:
   for j from 0 to 10 do:
      V1 := V * 10^(nops(S) + j) + i;
      if IsPalindromic(V1, Base) then
         A := [op(A), V1];
      fi;
   od:
   V1 := (V - (V mod 10)) * 10^(nops(S) - 1) + i;
   if IsPalindromic(V1, Base) then
      A := [op(A), V1];
   fi;
od:
sort(A);
  • Mathematica
    palQ[n_, b_] := Block[{d = IntegerDigits[n, b]}, If[d == Reverse@ d, True, False]]; Select[Range[0, 10^6], And[palQ[#, 10], palQ[#, 19]] &] (* Michael De Vlieger, Mar 07 2015 *)
b1=10; b2=19; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10^7}]; lst (* Vincenzo Librandi, Mar 08 2015 *)
  • PARI
    isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 19)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 07 2015
Previous Showing 31-36 of 36 results.

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