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A299755 Triangle read by rows in which row n is the strict integer partition with FDH number n. 28
1, 2, 3, 4, 2, 1, 5, 3, 1, 6, 4, 1, 7, 3, 2, 8, 5, 1, 4, 2, 9, 10, 6, 1, 11, 4, 3, 5, 2, 7, 1, 12, 3, 2, 1, 13, 8, 1, 6, 2, 5, 3, 14, 4, 2, 1, 15, 9, 1, 7, 2, 10, 1, 5, 4, 6, 3, 16, 11, 1, 8, 2, 4, 3, 1, 17, 5, 2, 1, 18, 7, 3, 6, 4, 12, 1, 19, 9, 2, 20, 13, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive integer n has a unique factorization of the form n = f(s_1)*...*f(s_k) where the s_i are strictly increasing positive integers. This determines a unique strict integer partition (s_k...s_1) whose FDH number is then defined to be n.

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

Sequence of strict integer partitions begins: () (1) (2) (3) (4) (2,1) (5) (3,1) (6) (4,1) (7) (3,2) (8) (5,1) (4,2) (9) (10) (6,1) (11) (4,3) (5,2) (7,1) (12) (3,2,1) (13) (8,1) (6,2) (5,3) (14) (4,2,1) (15).

MATHEMATICA

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)]]]]];

nn=200; FDprimeList=Array[FDfactor, nn, 1, Union];

FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];

Join@@Table[Reverse[FDfactor[n]/.FDrules], {n, nn}]

CROSSREFS

Row lengths are A064547.

Cf. A005117, A050376, A112798, A213925, A246867, A296150, A299756, A299757, A299759.

Sequence in context: A165052 A107474 A114734 * A323907 A214065 A182710

Adjacent sequences:  A299752 A299753 A299754 * A299756 A299757 A299758

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Feb 18 2018

STATUS

approved

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)