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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 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

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