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A060873 Intrinsic 3-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base. 13
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A333308 A179196 A024325 * A186542 A287444 A196175
KEYWORD
nonn,base
AUTHOR
Harvey P. Dale, May 05 2001
STATUS
approved

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Last modified May 18 19:36 EDT 2024. Contains 372666 sequences. (Running on oeis4.)