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 A178683 Shortest partition of n with maximal product, sorted descending & considered as a base-5 number. 1
 0, 1, 2, 3, 4, 17, 18, 23, 92, 93, 118, 467, 468, 593, 2342, 2343, 2968, 11717, 11718, 14843, 58592, 58593, 74218, 292967, 292968, 371093, 1464842, 1464843, 1855468, 7324217, 7324218, 9277343, 36621092, 36621093, 46386718, 183105467 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 E. W. Dijkstra, EWD Archive To hell with "meaningful identifiers" - EWD1044 Roger Hui & Boyko Bantchev, J Wiki An Essay on Partitions EXAMPLE For n=10: the integer 10 has 42 partitions (e.g., 7+1+1+1, 6+4, 4+3+3, ...). The products of these partitions range from 1 (1*1*1*...) to 36. There are only two partitions that have the maximal product of 36: (4,3,3) and (3,3,2,2). Of these, the former is shorter (3 elements vs 4). So 4,3,3 is the shortest maximal partition of 10. This partition, sorted descending and considered as a number in base 5 (where each element of the partition is a digit), is (4*5^2) + (3*5^1) + (3*5^0) = 118. Hence a(10) = 118. MAPLE a:= proc(n) local m, q, r; if n<5 then n else q:= iquo(n, 3, 'r'); m:= 3*(5^q-1)/4; if r=1 then m:= m +5^(q-1) elif r=2 then m:= m *5+2 fi; m fi end: seq(a(n), n=0..35); # Alois P. Heinz, Nov 26 2010 PROG (J) . aXXXX =: (5 #. ] {::~ [: (i. >./) */&>)@:part"0 . part =: 3 : 'final (, new)^:y <) @ > @ {: . new =: (-i.)@# <@:(cat&.>) ] . cat =: [ ; @:(, .&.>) -@(<.#) {. ] CROSSREFS Sequence in context: A300855 A353164 A333835 * A111191 A333825 A115891 Adjacent sequences: A178680 A178681 A178682 * A178684 A178685 A178686 KEYWORD base,easy,nonn AUTHOR Dan Bron (dan(AT)bron.us), Jun 03 2010 STATUS approved

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Last modified February 5 19:48 EST 2023. Contains 360087 sequences. (Running on oeis4.)