A325618 Numbers m such that there exists an integer partition of m whose reciprocal factorial sum is 1.

1, 4, 11, 18, 24, 31, 37, 44, 45, 50, 52, 57, 58, 65, 66, 70, 71, 73, 76, 78, 79, 83, 86, 87, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 107, 108, 109, 110, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 130, 131

Offset

1,2

Comments

The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.

Conjecture: 137 is the greatest integer not in this sequence. - Charlie Neder, May 14 2019

Links

Charlie Neder, Table of n, a(n) for n = 1..1000

Example

The sequence of terms together with an integer partition of each whose reciprocal factorial sum is 1 begins:
   1: (1)
   4: (2,2)
  11: (3,3,3,2)
  18: (3,3,3,3,3,3)
  24: (4,4,4,4,3,3,2)
  31: (4,4,4,4,3,3,3,3,3)
  37: (4,4,4,4,4,4,4,4,3,2)
  44: (4,4,4,4,4,4,4,4,3,3,3,3)
  45: (5,5,5,5,5,4,4,4,3,3,2)
  50: (4,4,4,4,4,4,4,4,4,4,4,4,2)

Crossrefs

Factorial numbers: A000142, A002982, A007489, A011371, A022559, A064986, A115627, A284605, A325616.

Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316855, A325619, A325620, A325621, A325622, A325623, A325624.

Sequence in context: A050395 A368424 A059771 * A361131 A043409 A030610

Adjacent sequences: A325615 A325616 A325617 * A325619 A325620 A325621

Keyword

nonn

Author

Gus Wiseman, May 13 2019

Extensions

a(11)-a(55) from Charlie Neder, May 14 2019

Status

approved