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.

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A265543 a(n) = smallest base-2 palindrome m >= n such that every base-2 digit of n is <= the corresponding digit of m; m is written in base 2.

Original entry on oeis.org

0, 1, 11, 11, 101, 101, 111, 111, 1001, 1001, 1111, 1111, 1111, 1111, 1111, 1111, 10001, 10001, 11011, 11011, 10101, 10101, 11111, 11111, 11011, 11011, 11011, 11011, 11111, 11111, 11111, 11111, 100001, 100001, 110011, 110011, 101101, 101101, 111111, 111111, 101101, 101101, 111111, 111111, 101101, 101101, 111111
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.
See A206913 for the values of m written in base 10.

Programs

  • Maple
    ispal:= proc(n) global b; # test if n is base-b palindrome
  local L, Ln, i;
  L:= convert(n, base, b);
  Ln:= nops(L);
for i from 1 to floor(Ln/2) do
if L[i] <> L[Ln+1-i] then return(false); fi;
od:
return(true);
end proc;
# find min pal >= n and with n in base-b shadow, write in base 10
over10:=proc(n) global b;
local t1,t2,i,m,sw1,L1;
t1:=convert(n,base,b);
L1:=nops(t1);
for m from n to 10*n do
if ispal(m) then
   t2:=convert(m,base,b);
   sw1:=1;
   for i from 1 to L1 do
      if t1[i] > t2[i] then sw1:=-1; break; fi;
                      od:
   if sw1=1 then return(m); fi;
fi;
                       od;
lprint("no solution in over10 for n = ", n);
end proc;
# find min pal >= n and with n in base-b shadow, write in base 10
overb:=proc(n) global b;
local t1,t2,i,m,mb,sw1,L1;
t1:=convert(n,base,b);
L1:=nops(t1);
for m from n to 10*n do
if ispal(m) then
   t2:=convert(m,base,b);
   sw1:=1;
   for i from 1 to L1 do
      if t1[i] > t2[i] then sw1:=-1; break; fi;
                      od:
   if sw1=1 then mb:=add(t2[i]*10^(i-1), i=1..nops(t2)); return(mb); fi;
fi;
                       od;
lprint("no solution in over10 for n = ", n);
end proc;
b:=2;
[seq(over10(n),n=0..144)]; # A175298
[seq(overb(n),n=0..144)]; # A265543
  • Mathematica
    sb2p[n_]:=Module[{m=n},While[!PalindromeQ[IntegerDigits[m,2]]|| Min[ IntegerDigits[ m,2]-IntegerDigits[n,2]]<0,m++];FromDigits[ IntegerDigits[ m,2]]]; Array[sb2p,50,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 15 2017 *)

A265558 a(n) = smallest base-10 palindrome m >= n such that every base-10 digit of n is <= the corresponding digit of m.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 22, 33, 44, 55, 66, 77, 88, 99, 22, 22, 22, 33, 44, 55, 66, 77, 88, 99, 33, 33, 33, 33, 44, 55, 66, 77, 88, 99, 44, 44, 44, 44, 44, 55, 66, 77, 88, 99, 55, 55, 55, 55, 55, 55, 66, 77, 88, 99, 66, 66, 66, 66, 66, 66, 66, 77, 88, 99, 77, 77, 77, 77, 77, 77, 77, 77, 88, 99, 88, 88
Offset: 0

Views

Author

N. J. A. Sloane, Dec 10 2015

Keywords

Links

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.
Cf. A265525.

Programs

  • Maple
    For Maple code see A265543.
  • PARI
    a(n,base=10) = { my (d=digits(n,base)); for (k=1, #d\2, d[k]=d[#d+1-k]=max(d[k],d[#d+1-k])); fromdigits(d,base) } \\ Rémy Sigrist, Jun 24 2022

A175917 Convert n to binary. NOR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.

Original entry on oeis.org

0, 0, 0, 0, 2, 2, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 14, 14, 4, 4, 10, 10, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 30, 30, 12, 12, 18, 18, 0, 0, 18, 18, 0, 0, 18, 18, 0, 0, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62, 62, 28, 28, 42, 42, 8, 8, 54, 54, 20, 20, 34, 34, 0, 0, 42, 42, 8, 8, 42, 42, 8, 8, 34
Offset: 0

Views

Author

Dylan Hamilton, Oct 15 2010

Keywords

Comments

Description format taken from Leroy Quet's OR and AND gate sequences for consistency.

Links

Crossrefs

Or A175298 and And A175297 gate sequences. The rest of the equivalent sequences for other gates are adjacent.

Programs

  • Mathematica
    Table[f = IntegerDigits[x, 2]; f = f + Reverse[f]; FromDigits[ Table[If[Positive[f[[r]]], 0, 1], {r, 1, Length[f]}], 2], {x, STARTPOINT,ENDPOINT}]

A175918 Convert n to binary. NAND each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.

Original entry on oeis.org

0, 0, 3, 0, 7, 2, 5, 0, 15, 6, 15, 6, 15, 6, 9, 0, 31, 14, 31, 14, 27, 10, 27, 10, 31, 14, 21, 4, 27, 10, 17, 0, 63, 30, 63, 30, 63, 30, 63, 30, 63, 30, 63, 30, 51, 18, 51, 18, 63, 30, 45, 12, 63, 30, 45, 12, 63, 30, 45, 12, 51, 18, 33, 0, 127, 62, 127, 62, 127, 62, 127, 62, 119, 54, 119
Offset: 0

Views

Author

Dylan Hamilton, Oct 15 2010

Keywords

Comments

Description format taken from Leroy Quet's OR and AND gate sequences for consistency.

Links

Crossrefs

Or A175298 and And A175297 gate sequences. The rest of the equivalent sequences for other gates are adjacent.

Programs

  • Mathematica
    Table[f = IntegerDigits[x, 2]; f = f + Reverse[f]; FromDigits[ Table[If[f[[r]] < 2, 1, 0], {r, 1, Length[f]}], 2], {x, STARTPOINT,ENDPOINT}]

A175920 Convert n to binary. XNOR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.

Original entry on oeis.org

0, 1, 0, 3, 2, 7, 2, 7, 6, 15, 0, 9, 0, 9, 6, 15, 14, 31, 4, 21, 14, 31, 4, 21, 4, 21, 14, 31, 4, 21, 14, 31, 30, 63, 12, 45, 18, 51, 0, 33, 18, 51, 0, 33, 30, 63, 12, 45, 12, 45, 30, 63, 0, 33, 18, 51, 0, 33, 18, 51, 12, 45, 30, 63, 62, 127, 28, 93, 42, 107, 8, 73, 62, 127, 28, 93, 42
Offset: 0

Views

Author

Dylan Hamilton, Oct 15 2010

Keywords

Comments

Description format taken from Leroy Quet's OR and AND gate sequences for consistency.

Links

Crossrefs

Or A175298 and And A175297 gate sequences. The rest of the equivalent sequences for other gates are adjacent.

Programs

  • Mathematica
    Table[f = IntegerDigits[x, 2]; f = f + Reverse[f]; FromDigits[ Table[If[EvenQ[f[[r]]], 1, 0], {r, 1, Length[f]}], 2], {x, STARTPOINT,ENDPOINT}]

A265511 a(n) = largest base-3 palindrome m <= n such that every base-3 digit of m is <= the corresponding digit of n; m is written in base 10.

Original entry on oeis.org

0, 1, 2, 0, 4, 4, 0, 4, 8, 0, 10, 10, 0, 13, 13, 0, 16, 16, 0, 10, 20, 0, 13, 23, 0, 16, 26, 0, 28, 28, 0, 28, 28, 0, 28, 28, 0, 28, 28, 0, 40, 40, 0, 40, 40, 0, 28, 28, 0, 40, 40, 0, 52, 52, 0, 28, 56, 0, 28, 56, 0, 28, 56, 0, 28, 56, 0, 40, 68, 0, 40, 68, 0, 28, 56, 0, 40, 68, 0, 52, 80, 0, 82, 82, 0, 82, 82, 0, 82
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Links

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

Programs

  • Maple
    F:= proc(n) local L;
  L:= convert(n,base,3);
  if L[1] = 0 then return 0 fi;
  add(min(L[i],L[-i])*3^(i-1),i=1..nops(L))
end proc:
map(F, [$0..100]); # Robert Israel, Jan 13 2020

A265523 a(n) = largest base-9 palindrome m <= n such that every base-9 digit of m is <= the corresponding digit of n; m is written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 10, 10, 10, 10, 10, 10, 10, 10, 0, 10, 20, 20, 20, 20, 20, 20, 20, 0, 10, 20, 30, 30, 30, 30, 30, 30, 0, 10, 20, 30, 40, 40, 40, 40, 40, 0, 10, 20, 30, 40, 50, 50, 50, 50, 0, 10, 20, 30, 40, 50, 60, 60, 60, 0, 10, 20, 30, 40, 50, 60, 70, 70, 0, 10, 20, 30, 40, 50, 60, 70, 80, 0, 82, 82
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Links

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

Programs

  • Maple
    F:= proc(n) local L;
  L:= convert(n,base,9);
if L[1] = 0 then return 0 fi;
  add(min(L[i],L[-i])*9^(i-1),i=1..nops(L))
end proc:
map(F, [$0..100]); # Robert Israel, Jan 13 2020

A265526 Largest base-2 palindrome m <= n, written in base 2.

Original entry on oeis.org

0, 1, 1, 11, 11, 101, 101, 111, 111, 1001, 1001, 1001, 1001, 1001, 1001, 1111, 1111, 10001, 10001, 10001, 10001, 10101, 10101, 10101, 10101, 10101, 10101, 11011, 11011, 11011, 11011, 11111, 11111, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 100001, 101101, 101101, 101101
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

Programs

  • Maple
    ispal:= proc(n) global b; # test for base-b palindrome
  local L, Ln, i;
  L:= convert(n, base, b);
  Ln:= nops(L);
for i from 1 to floor(Ln/2) do
if L[i] <> L[Ln+1-i] then return(false); fi;
od:
return(true);
end proc;
# find max pal <= n, write in base 10
less10:=proc(n) global b;
local t1,t2,i,m,sw1,L2;
t1:=convert(n,base,b);
for m from n by -1 to 0 do
if ispal(m) then return(m); fi;
                        od;
end proc;
# find max pal <= n, write in base b
lessb:=proc(n) global b;
local t1,t2,i,m,mb,sw1,L2;
t1:=convert(n,base,b);
for m from n by -1 to 0 do
if ispal(m) then
   t2:=convert(m,base,b);
   L2:=nops(t2);
   mb:=add(t2[i]*10^(i-1), i=1..L2); return(mb); fi;
                        od;
end proc;
b:=2;
[seq(less10(n),n=0..100)]; # A206913
[seq(lessb(n),n=0..100)]; # A265526
[seq(less10(2*n),n=0..100)]; # A265527
[seq(lessb(2*n),n=0..100)]; # A265528
b:=10;
[seq(less10(n),n=0..100)]; # A261423

A265527 Largest base-2 palindrome m <= 2n, written in base 10.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 9, 9, 15, 17, 17, 21, 21, 21, 27, 27, 31, 33, 33, 33, 33, 33, 33, 45, 45, 45, 51, 51, 51, 51, 51, 51, 63, 65, 65, 65, 65, 73, 73, 73, 73, 73, 73, 85, 85, 85, 85, 93, 93, 93, 99, 99, 99, 99, 107, 107, 107, 107, 107, 107, 119, 119, 119, 119, 127, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

A265528 Largest base-2 palindrome m <= 2n, written in base 2.

Original entry on oeis.org

0, 1, 11, 101, 111, 1001, 1001, 1001, 1111, 10001, 10001, 10101, 10101, 10101, 11011, 11011, 11111, 100001, 100001, 100001, 100001, 100001, 100001, 101101, 101101, 101101, 110011, 110011, 110011, 110011, 110011, 110011, 111111, 1000001, 1000001, 1000001, 1000001, 1001001, 1001001, 1001001, 1001001, 1001001, 1001001
Offset: 0

Views

Author

N. J. A. Sloane, Dec 09 2015

Keywords

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.
Previous Showing 11-20 of 75 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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