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 A117118 Number of partitions of n into consecutive parts containing no binary powers. 0
 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 3, 3, 1, 3, 1, 2, 3, 2, 1, 2, 0, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 4, 1, 2, 3, 2, 1, 3, 2, 2, 3, 2, 2, 3, 1, 2, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 3, 2, 1, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS a(n) <= A001227(n). LINKS Table of n, a(n) for n=1..105. EXAMPLE a(60) = #{10+11+12+13+14, 19+20+21, 60} = 3, 4+5+6+7+8+9+10+11=60 doesn't count because 4=2^2 or 8=2^3. MATHEMATICA a[n_] := a[n] = Count[IntegerPartitions[n, All, Cases[Range[3, n], k_Integer /; Total[IntegerDigits[k, 2]] > 1]], q_List /; Length[q] == Length[Union[q]] && Length[q] == First[q] - Last[q] + 1]; Table[Print[n, " ", a[n]]; a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 06 2021 *) CROSSREFS Cf. A001227, A118164. Sequence in context: A280737 A322305 A020951 * A117168 A355343 A287160 Adjacent sequences: A117115 A117116 A117117 * A117119 A117120 A117121 KEYWORD nonn AUTHOR Reinhard Zumkeller, Apr 17 2006 STATUS approved

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Last modified May 29 13:20 EDT 2023. Contains 363042 sequences. (Running on oeis4.)