A060873 - OEIS

%I #19 Jan 05 2025 19:51:36

%S 5,7,10,13,16,17,20,21,23,25,26,29,31,34,36,37,38,41,42,43,46,49,50,

%T 51,52,55,57,59,61,62,63,64,65,67,71,72,73,74,78,80,81,82,83,85,86,88,

%U 89,91,92,93,97,98,100,101,104,105,107,109,111,113,114,117,118

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

%C 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.

%H Jean-François Alcover, <a href="/A060873/b060873.txt">Table of n, a(n) for n = 1..1000</a>

%H A. J. Di Scala and M. Sombra, <a href="http://arXiv.org/abs/math.GM/0105022">Intrinsic Palindromic Numbers</a>, arXiv:math/0105022 [math.GM], 2001.

%H A. J. Di Scala and M. Sombra, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-1/quartscala01_2004.pdf">Intrinsic Palindromes</a>, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

%t 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 *)

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

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, May 05 2001