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A299755
Triangle read by rows in which row n is the strict integer partition with FDH number n.
38
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
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.
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
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Feb 18 2018
STATUS
approved