A117118 Number of partitions of n into consecutive parts containing no binary powers.

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

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