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Revision History for A319855

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A319855

Minimum number that can be obtained by iteratively adding or multiplying together parts of the integer partition with Heinz number n until only one part remains.
(history; published version)

#10 by Michel Marcus at Thu Oct 04 10:15:32 EDT 2018

STATUS

reviewed

approved

#9 by Joerg Arndt at Thu Oct 04 10:14:40 EDT 2018

STATUS

proposed

reviewed

#8 by Charlie Neder at Wed Oct 03 17:42:22 EDT 2018

STATUS

editing

proposed

#7 by Charlie Neder at Wed Oct 03 17:37:14 EDT 2018

FORMULA

a(1) = 0, a(n) = max(A056239(n) - A007814(n), 1). - Charlie Neder, Oct 03 2018

STATUS

approved

editing

#6 by Susanna Cuyler at Sun Sep 30 20:27:03 EDT 2018

STATUS

proposed

approved

#5 by Gus Wiseman at Sat Sep 29 12:40:16 EDT 2018

STATUS

editing

proposed

#4 by Gus Wiseman at Sat Sep 29 12:34:56 EDT 2018

CROSSREFS

Cf. A000792, A001970, A048249, A056239, A066739, A066815, A070960, A201163, A319850, A318948, A318949, A319841, A319856.

#3 by Gus Wiseman at Sat Sep 29 12:29:18 EDT 2018

CROSSREFS

Cf. A000792, A001970, A048249, A066739, A066815, A070960, A201163, A319850, A318948, A318949, A319841, A319856.

#2 by Gus Wiseman at Sat Sep 29 12:26:29 EDT 2018

NAME

allocated for Gus WisemanMinimum number that can be obtained by iteratively adding or multiplying together parts of the integer partition with Heinz number n until only one part remains.

DATA

0, 1, 2, 1, 3, 2, 4, 1, 4, 3, 5, 2, 6, 4, 5, 1, 7, 4, 8, 3, 6, 5, 9, 2, 6, 6, 6, 4, 10, 5, 11, 1, 7, 7, 7, 4, 12, 8, 8, 3, 13, 6, 14, 5, 7, 9, 15, 2, 8, 6, 9, 6, 16, 6, 8, 4, 10, 10, 17, 5, 18, 11, 8, 1, 9, 7, 19, 7, 11, 7, 20, 4, 21, 12, 8, 8, 9, 8, 22, 3, 8

OFFSET

1,3

COMMENTS

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

EXAMPLE

a(30) = 5 because the minimum number that can be obtained starting with (3,2,1) is 3+2*1 = 5.

MATHEMATICA

ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]];

nexos[ptn_]:=If[Length[ptn]==0, {0}, Union@@Select[ReplaceListRepeated[{Sort[ptn]}, {{foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x+y]], {foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]];

Table[Min[nexos[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], {n, 100}]

CROSSREFS

Cf. A000792, A001970, A048249, A066739, A066815, A070960, A201163, A319850, A318948, A318949, A319841.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Sep 29 2018

STATUS

approved

editing

#1 by Gus Wiseman at Sat Sep 29 12:26:29 EDT 2018

NAME

allocated for Gus Wiseman

KEYWORD

allocated

STATUS

approved