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 A298481 a(n) is the number of ways to partition the binary representation of n into the minimal number of palindromic parts. 1
 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS A minimal palindromic partition is a partition of the string into palindromes with the fewest parts. A298475(n) gives the size of the minimal partition of the binary representation of n. Records occur at 1, 10, 42, 170, 682, 1357, 5428, 5453, 21812, 21837, 45746, .... LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 EXAMPLE The a(n) minimal palindromic partitions for five integers:   n | a(n) | A298475(n) | binary   | partitions ----+------+------------+----------+-------------------------------------- 2   | 1    | 2          | 10       | 1'0 5   | 1    | 1          | 101      | 101 10  | 2    | 2          | 1010     | 101'0 or 1'010 37  | 2    | 3          | 100101   | 1001'0'1 or 1'00'101 149 | 3    | 3          | 10010101 | 1001'010'1, 1'00'10101, or 1001'0'101 MATHEMATICA {1, 1}~Join~Array[Function[w, Length@ MinimalBy[#, Length] &@ Select[#, And[AllTrue[#, PalindromeQ], Union@ Map[Length, #] != {1}] &] &@ Union@ Map[Select[SplitBy[#, IntegerQ], IntegerQ@ First@ # &] &, Map[Insert[w, ".", #] &, Map[{#} &, Rest@ Subsets@ Range@ Length@ w, {2}]]]]@ IntegerDigits[#, 2] &, 103, 3] (* Michael De Vlieger, Jan 23 2018 *) CROSSREFS Cf. A298475. Sequence in context: A288120 A156264 A249770 * A324872 A307608 A323022 Adjacent sequences:  A298478 A298479 A298480 * A298482 A298483 A298484 KEYWORD nonn,base AUTHOR Peter Kagey, Jan 19 2018 STATUS approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)