A060873 -id:A060873 - cp's OEIS frontend

A060879 Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

257, 273, 297, 313, 325, 341, 365, 381, 387, 403, 427, 443, 455, 471, 495, 511, 6562, 6643, 6724, 6832, 6913, 6994, 7102, 7183, 7264, 7300, 7381, 7462, 7570, 7651, 7732, 7840, 7921, 8002, 8038, 8119, 8200, 8308, 8389, 8470, 8578, 8659

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and (for n>2) 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4. - Franklin T. Adams-Watters, Jul 29 2011

Peter Kagey, Table of n, a(n) for n = 1..10000
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873, A060874, A060875, A060876, A060877, A060878, A060947, A060948, A060949.

A060947 Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

513, 561, 585, 633, 645, 693, 717, 765, 771, 819, 843, 891, 903, 951, 975, 1023, 19684, 20008, 20332, 20440, 20764, 21088, 21196, 21520, 21844, 21880, 22204, 22528, 22636, 22960, 23284, 23392, 23716, 24040, 24076, 24400, 24724, 24832

Offset: 1

Harvey P. Dale, May 08 2001

See A060873 for more information.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A060873-A060879.

testQ[n_, k_] := For[b = 2, b <= Ceiling[(n-1)^(1/(k-1))], b++, d = IntegerDigits[n, b]; If[Length[d] == k && d == Reverse[d], Return[True]]]; n0[k_] := 2^(k-1) + 1; Reap[Do[If[testQ[n, 10] === True, Print[n, " ", FromDigits[d], " b = ", b]; Sow[n]], {n, n0[10], 25000}]][[2, 1]] (* Jean-François Alcover, Nov 07 2014 *)

A060949 Intrinsic 12-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

2049, 2145, 2193, 2289, 2313, 2409, 2457, 2553, 2565, 2661, 2709, 2805, 2829, 2925, 2973, 3069, 3075, 3171, 3219, 3315, 3339, 3435, 3483, 3579, 3591, 3687, 3735, 3831, 3855, 3951, 3999, 4095, 177148, 178120, 179092, 179416, 180388

Offset: 1

Harvey P. Dale, May 08 2001

See A060873 for more information.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A060873-A060879.

A060874 Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

9, 15, 28, 40, 52, 56, 65, 68, 80, 85, 105, 125, 126, 130, 150, 156, 170, 186, 190, 195, 215, 216, 217, 235, 246, 252, 255, 259, 282, 301, 312, 342, 343, 344, 372, 378, 385, 400, 408, 427, 434, 438, 456, 468, 476, 498, 504, 512, 513, 518, 534

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Robert Israel and Peter Kagey, Table of n, a(n) for n = 1..10000 (1..1000 from Peter Kagey)
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873-A060879, A060947-A060949.

N:= 10^4: # to get all terms <= N
S:= {}:
for b from 2 to floor(N^(1/3)) do
  S:= S union {seq(seq((b^3+1)*i+(b^2+b)*j,j=0..b-1),i=1..b-1)}
od:
sort(convert(select(`<=`,S,N),list)); # Robert Israel, May 23 2016

A060875 Intrinsic 5-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

17, 21, 27, 31, 82, 91, 100, 112, 121, 130, 142, 151, 160, 164, 173, 182, 194, 203, 212, 224, 233, 242, 257, 273, 289, 305, 325, 341, 357, 373, 393, 409, 425, 441, 461, 477, 493, 509, 514, 530, 546, 562, 582, 598, 614, 626, 630, 650, 651, 666

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Peter Kagey, Table of n, a(n) for n = 1..10000
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873, A060874, A060876, A060877, A060878, A060879, A060947, A060948, A060949.

A060876 Intrinsic 6-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

33, 45, 51, 63, 244, 280, 316, 328, 364, 400, 412, 448, 484, 488, 524, 560, 572, 608, 644, 656, 692, 728, 1025, 1105, 1185, 1265, 1285, 1365, 1445, 1525, 1545, 1625, 1705, 1785, 1805, 1885, 1965, 2045, 2050, 2130, 2210, 2290, 2310, 2390

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Peter Kagey, Table of n, a(n) for n = 1..10000
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873, A060874, A060875, A060877, A060878, A060879, A060947, A060948, A060949.

A060877 Intrinsic 7-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

65, 73, 85, 93, 99, 107, 119, 127, 730, 757, 784, 820, 847, 874, 910, 937, 964, 976, 1003, 1030, 1066, 1093, 1120, 1156, 1183, 1210, 1222, 1249, 1276, 1312, 1339, 1366, 1402, 1429, 1456, 1460, 1487, 1514, 1550, 1577, 1604, 1640, 1667, 1694

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Peter Kagey, Table of n, a(n) for n = 1..10000
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873, A060874, A060875, A060876, A060878, A060879, A060947, A060947, A060949.

A060878 Intrinsic 8-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

129, 153, 165, 189, 195, 219, 231, 255, 2188, 2296, 2404, 2440, 2548, 2656, 2692, 2800, 2908, 2920, 3028, 3136, 3172, 3280, 3388, 3424, 3532, 3640, 3652, 3760, 3868, 3904, 4012, 4120, 4156, 4264, 4372, 4376, 4484, 4592, 4628, 4736, 4844

Offset: 1

Harvey P. Dale, May 05 2001

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Peter Kagey, Table of n, a(n) for n = 1..10000
A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Cf. A060873, A060874, A060875, A060876, A060877, A060879, A060947, A060948, A060949.

A060948 Intrinsic 11-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Original entry on oeis.org

1025, 1057, 1105, 1137, 1161, 1193, 1241, 1273, 1285, 1317, 1365, 1397, 1421, 1453, 1501, 1533, 1539, 1571, 1619, 1651, 1675, 1707, 1755, 1787, 1799, 1831, 1879, 1911, 1935, 1967, 2015, 2047, 59050, 59293, 59536, 59860, 60103, 60346

Offset: 1

Harvey P. Dale, May 08 2001

See A060873 for more information.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A060873-A060879.

A114255 Numbers that are nontrivial (3 digits or more) palindromes when expressed in some base 2 or greater.

Original entry on oeis.org

5, 7, 9, 10, 13, 15, 16, 17, 20, 21, 23, 25, 26, 27, 28, 29, 31, 33, 34, 36, 37, 38, 40, 41, 42, 43, 45, 46, 49, 50, 51, 52, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 71, 72, 73, 74, 78, 80, 81, 82, 83, 85, 86, 88, 89, 91, 92, 93, 97, 98, 99, 100, 101, 104, 105, 107, 109

Offset: 1

Jason Orendorff (jason.orendorff(AT)gmail.com), Feb 05 2006

All integers are trivially palindromes in base 1. All integers n>2 are trivially 2-digit palindromes because they can be represented as "11" in base n-1.

			5 is present because the palindrome (101 base 2) = 5; 803 is present because (30203 base 4) = 803.

Cf. A060873-A060879, A060947-A060949, A123586.

isPalindrome s = (s == reverse s) digits 0 _ = [] digits n b = n `rem` b : digits (n `quot` b) b check n = any isPalindrome $ takeWhile (\x -> length x > 2) $ map (digits n) [2..] main = mapM print $ filter check [1..]

palindromeQ[n_, b_] := (id = IntegerDigits[n, b]) === Reverse[id] && Length[id] >= 3; palindromeQ[n_] := Or @@ (palindromeQ[n, #] & ) /@ Range[2, n-2]; Select[ Range[110], palindromeQ] (* Jean-François Alcover, Dec 16 2011 *)

isok(n) = for (b=2, n-1, if ((d=digits(n,b)) && (#d >= 3) && (Vecrev(d) == d), return (1));); \\ Michel Marcus, Jul 28 2016

Cross-references from Charles R Greathouse IV, Aug 04 2010

cp's OEIS Frontend

A060879 Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060947 Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A060949 Intrinsic 12-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060874 Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

A060875 Intrinsic 5-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060876 Intrinsic 6-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060877 Intrinsic 7-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060878 Intrinsic 8-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A060948 Intrinsic 11-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

Views

Author

Keywords

Comments

Links

Crossrefs

A114255 Numbers that are nontrivial (3 digits or more) palindromes when expressed in some base 2 or greater.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Haskell

Mathematica

PARI

Extensions