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A316267 FDH numbers of strict integer partitions of prime numbers with a prime number of prime parts. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A325301 A219542 A137480 * A228766 A157157 A218043

Adjacent sequences:  A316264 A316265 A316266 * A316268 A316269 A316270

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 28 2018

STATUS

approved

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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)