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

1,1

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.

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 *)

Crossrefs

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

Sequence in context: A333308 A179196 A024325 * A186542 A287444 A196175

Adjacent sequences: A060870 A060871 A060872 * A060874 A060875 A060876

Keyword

nonn,base

Author

Harvey P. Dale, May 05 2001

Status

approved