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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 (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
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.
Sequence in context: A165052 A107474 A114734 * A323907 A214065 A182710
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Feb 18 2018
STATUS
approved

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)