A060873 Intrinsic 3-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

5, 7, 10, 13, 16, 17, 20, 21, 23, 25, 26, 29, 31, 34, 36, 37, 38, 41, 42, 43, 46, 49, 50, 51, 52, 55, 57, 59, 61, 62, 63, 64, 65, 67, 71, 72, 73, 74, 78, 80, 81, 82, 83, 85, 86, 88, 89, 91, 92, 93, 97, 98, 100, 101, 104, 105, 107, 109, 111, 113, 114, 117, 118

Offset: 1

Author

Harvey P. Dale, May 05 2001

Keywords

• nonn
• base

Comments

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

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000
• 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.

Crossrefs

Cf. A060874-A060879, A060947-A060949, A123586, A114255.

Programs

Mathematica

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, 3] === True, Print[n, " ", FromDigits[d], " b = ", b]; Sow[n]], {n, n0[3], 200}]][[2, 1]] (* Jean-François Alcover, Nov 07 2014 *)