A316267 FDH numbers of strict integer partitions of prime numbers with a prime number of prime parts.

12, 21, 57, 123, 249, 417, 532, 699, 867, 1100, 1389, 1463, 1509, 1708, 2049, 2068, 2307, 2324, 2913, 3116, 3147, 3157, 3273, 3325, 3619, 3903, 4227, 4268, 4636, 4821, 5079, 5225, 5324, 5516, 5739, 6308, 6391, 6524, 6621, 6644, 7469, 8092, 8193, 8225, 8457

Offset

1,1

Comments

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1,...,y_k) is f(y_1)*...*f(y_k).

Links

Table of n, a(n) for n=1..45.

Example

Sequence of strict integer partitions of prime numbers with a prime number of prime parts, preceded by their FDH numbers, begins:
    12: (3,2)
    21: (5,2)
    57: (11,2)
   123: (17,2)
   249: (29,2)
   417: (41,2)
   532: (11,5,3)
   699: (59,2)
   867: (71,2)
  1100: (13,7,3)
  1389: (101,2)
  1463: (11,7,5)
  1509: (107,2)
  1708: (23,5,3)

Mathematica

nn=1000;
FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];
FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], And[PrimeQ[Total[FDfactor[#]/.FDrules]], PrimeQ[Length[FDfactor[#]]], And@@PrimeQ/@(FDfactor[#]/.FDrules)]&]

Crossrefs

Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316265, A316266.

Sequence in context: A354984 A367357 A137480 * A228766 A157157 A218043

Adjacent sequences: A316264 A316265 A316266 * A316268 A316269 A316270

Keyword

nonn

Author

Gus Wiseman, Jun 28 2018

Status

approved