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 A308657 Smallest number that is nontrivially palindromic in n consecutive number bases. 0
 3, 10, 178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Nontrivially palindromic means having at least 2 digits in the palindromic base representation. | n | term | consecutive palindromic bases representations | +---+------+-----------------------------------------------+ | 1 | 3 | 11_2 | | 2 | 10 | 101_3 = 22_4 | | 3 | 178 | 454_6 = 343_7 = 262_8 | It is not known if the fourth term exists. The problem can be looked at in context of Diophantine equations, which seem hard. LINKS EXAMPLE a(1) = 3 because it is the smallest nontrivial palindrome in some number base: 11 when written in binary. a(2) = A279092(1) = 10 because it is the smallest nontrivial palindrome in two consecutive number bases, namely, bases 3 and 4: 101 and 22 when written in those number bases, respectively. a(3) = A279093(1) = 178 since it can be written as a palindrome, in three consecutive number bases, and it is the smallest such number. Those bases are 6, 7, 8 and those representations are 454, 343, 262. MATHEMATICA aQ[n_, m_] := SequenceCount[Length[(d = IntegerDigits[n, #])] > 1 && PalindromeQ[d] & /@ Range[2, Ceiling[Sqrt[n]]], Table[True, {m}]] > 0; a[m_] := Module[{n = 2}, While[!aQ[n, m], n++]; n]; Array[a, 3] (* Amiram Eldar, Jul 19 2019 *) CROSSREFS Cf. A002113 (palindromes in base 10). Cf. A279092, A279093 (numbers that are nontrivially palindromic in k or more consecutive integer bases with k=2,3; for k>=4, no examples are known). Sequence in context: A067999 A256164 A270553 * A156193 A119035 A359554 Adjacent sequences: A308654 A308655 A308656 * A308658 A308659 A308660 KEYWORD nonn,bref,hard,base AUTHOR Matej Veselovac, Jun 14 2019 STATUS approved

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Last modified March 31 11:51 EDT 2023. Contains 361648 sequences. (Running on oeis4.)