A206914 -id:A206914 - cp's OEIS frontend

A265559 Smallest base-2 palindrome m >= n, written in base 2.

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

Offset: 0

N. J. A. Sloane, Dec 10 2015

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

See A206914 for the values of m written in base 10.

ispal:= proc(n) global b; # test if n is base-b pallindrome
  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, write in base 10
big10:=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 return(m); fi;
                       od;
lprint("no solution in big10 for n = ", n);
end proc;
# find min pal >= n, write in base 10
bigb:=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); mb:=add(t2[i]*10^(i-1), i=1..nops(t2)); return(mb); fi;
                       od;
lprint("no solution in big10 for n = ", n);
end proc;
b:=2;
[seq(big10(n),n=0..144)]; # A206914
[seq(bigb(n),n=0..144)]; # A265559

b2pal[n_]:=Module[{m=n},While[IntegerDigits[m,2]!=Reverse[IntegerDigits[m,2]],m++]; FromDigits[ IntegerDigits[m,2]]]; Array[b2pal,50,0] (* Harvey P. Dale, Feb 25 2024 *)

A265512 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 3.

Original entry on oeis.org

0, 1, 2, 0, 11, 11, 0, 11, 22, 0, 101, 101, 0, 111, 111, 0, 121, 121, 0, 101, 202, 0, 111, 212, 0, 121, 222, 0, 1001, 1001, 0, 1001, 1001, 0, 1001, 1001, 0, 1001, 1001, 0, 1111, 1111, 0, 1111, 1111, 0, 1001, 1001, 0, 1111, 1111, 0, 1221, 1221, 0, 1001, 2002, 0, 1001, 2002, 0, 1001, 2002, 0, 1001, 2002, 0, 1111, 2112

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265513 a(n) = largest base-4 palindrome m <= n such that every base-4 digit of m is <= the corresponding digit of n; m is written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 0, 5, 5, 5, 0, 5, 10, 10, 0, 5, 10, 15, 0, 17, 17, 17, 0, 21, 21, 21, 0, 25, 25, 25, 0, 29, 29, 29, 0, 17, 34, 34, 0, 21, 38, 38, 0, 25, 42, 42, 0, 29, 46, 46, 0, 17, 34, 51, 0, 21, 38, 55, 0, 25, 42, 59, 0, 29, 46, 63, 0, 65, 65, 65, 0, 65, 65, 65, 0, 65, 65, 65, 0, 65, 65, 65, 0, 65, 65, 65, 0, 85, 85

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265514 a(n) = largest base-4 palindrome m <= n such that every base-4 digit of m is <= the corresponding digit of n; m is written in base 4.

Original entry on oeis.org

0, 1, 2, 3, 0, 11, 11, 11, 0, 11, 22, 22, 0, 11, 22, 33, 0, 101, 101, 101, 0, 111, 111, 111, 0, 121, 121, 121, 0, 131, 131, 131, 0, 101, 202, 202, 0, 111, 212, 212, 0, 121, 222, 222, 0, 131, 232, 232, 0, 101, 202, 303, 0, 111, 212, 313, 0, 121, 222, 323, 0, 131, 232, 333, 0, 1001, 1001, 1001, 0, 1001, 1001, 1001, 0

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265515 a(n) = largest base-5 palindrome m <= n such that every base-5 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, 0, 6, 6, 6, 6, 0, 6, 12, 12, 12, 0, 6, 12, 18, 18, 0, 6, 12, 18, 24, 0, 26, 26, 26, 26, 0, 31, 31, 31, 31, 0, 36, 36, 36, 36, 0, 41, 41, 41, 41, 0, 46, 46, 46, 46, 0, 26, 52, 52, 52, 0, 31, 57, 57, 57, 0, 36, 62, 62, 62, 0, 41, 67, 67, 67, 0, 46, 72, 72, 72, 0, 26, 52, 78, 78, 0, 31, 57, 83, 83, 0, 36

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265516 a(n) = largest base-5 palindrome m <= n such that every base-5 digit of m is <= the corresponding digit of n; m is written in base 5.

Original entry on oeis.org

0, 1, 2, 3, 4, 0, 11, 11, 11, 11, 0, 11, 22, 22, 22, 0, 11, 22, 33, 33, 0, 11, 22, 33, 44, 0, 101, 101, 101, 101, 0, 111, 111, 111, 111, 0, 121, 121, 121, 121, 0, 131, 131, 131, 131, 0, 141, 141, 141, 141, 0, 101, 202, 202, 202, 0, 111, 212, 212, 212, 0, 121, 222, 222, 222, 0, 131, 232, 232, 232, 0, 141, 242, 242, 242

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265517 a(n) = largest base-6 palindrome m <= n such that every base-6 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, 0, 7, 7, 7, 7, 7, 0, 7, 14, 14, 14, 14, 0, 7, 14, 21, 21, 21, 0, 7, 14, 21, 28, 28, 0, 7, 14, 21, 28, 35, 0, 37, 37, 37, 37, 37, 0, 43, 43, 43, 43, 43, 0, 49, 49, 49, 49, 49, 0, 55, 55, 55, 55, 55, 0, 61, 61, 61, 61, 61, 0, 67, 67, 67, 67, 67, 0, 37, 74, 74, 74, 74, 0, 43, 80, 80, 80, 80, 0, 49, 86

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265518 a(n) = largest base-6 palindrome m <= n such that every base-6 digit of m is <= the corresponding digit of n; m is written in base 6.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 0, 11, 11, 11, 11, 11, 0, 11, 22, 22, 22, 22, 0, 11, 22, 33, 33, 33, 0, 11, 22, 33, 44, 44, 0, 11, 22, 33, 44, 55, 0, 101, 101, 101, 101, 101, 0, 111, 111, 111, 111, 111, 0, 121, 121, 121, 121, 121, 0, 131, 131, 131, 131, 131, 0, 141, 141, 141, 141, 141, 0, 151, 151, 151, 151, 151, 0, 101, 202, 202

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265519 a(n) = largest base-7 palindrome m <= n such that every base-7 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, 0, 8, 8, 8, 8, 8, 8, 0, 8, 16, 16, 16, 16, 16, 0, 8, 16, 24, 24, 24, 24, 0, 8, 16, 24, 32, 32, 32, 0, 8, 16, 24, 32, 40, 40, 0, 8, 16, 24, 32, 40, 48, 0, 50, 50, 50, 50, 50, 50, 0, 57, 57, 57, 57, 57, 57, 0, 64, 64, 64, 64, 64, 64, 0, 71, 71, 71, 71, 71, 71, 0, 78, 78, 78, 78, 78, 78, 0, 85, 85

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

A265520 a(n) = largest base-7 palindrome m <= n such that every base-7 digit of m is <= the corresponding digit of n; m is written in base 7.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 0, 11, 11, 11, 11, 11, 11, 0, 11, 22, 22, 22, 22, 22, 0, 11, 22, 33, 33, 33, 33, 0, 11, 22, 33, 44, 44, 44, 0, 11, 22, 33, 44, 55, 55, 0, 11, 22, 33, 44, 55, 66, 0, 101, 101, 101, 101, 101, 101, 0, 111, 111, 111, 111, 111, 111, 0, 121, 121, 121, 121, 121, 121, 0, 131, 131, 131, 131, 131, 131, 0

Offset: 0

N. J. A. Sloane, Dec 09 2015

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

cp's OEIS Frontend

A265559 Smallest base-2 palindrome m >= n, written in base 2.

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A265512 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 3.

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A265513 a(n) = largest base-4 palindrome m <= n such that every base-4 digit of m is <= the corresponding digit of n; m is written in base 10.

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A265514 a(n) = largest base-4 palindrome m <= n such that every base-4 digit of m is <= the corresponding digit of n; m is written in base 4.

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A265515 a(n) = largest base-5 palindrome m <= n such that every base-5 digit of m is <= the corresponding digit of n; m is written in base 10.

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A265516 a(n) = largest base-5 palindrome m <= n such that every base-5 digit of m is <= the corresponding digit of n; m is written in base 5.

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A265517 a(n) = largest base-6 palindrome m <= n such that every base-6 digit of m is <= the corresponding digit of n; m is written in base 10.

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A265518 a(n) = largest base-6 palindrome m <= n such that every base-6 digit of m is <= the corresponding digit of n; m is written in base 6.

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A265519 a(n) = largest base-7 palindrome m <= n such that every base-7 digit of m is <= the corresponding digit of n; m is written in base 10.

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A265520 a(n) = largest base-7 palindrome m <= n such that every base-7 digit of m is <= the corresponding digit of n; m is written in base 7.

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