A318993 Matula-Goebel number of the planted achiral tree determined by the n-th number whose consecutive prime indices are divisible.

1, 2, 4, 3, 8, 7, 16, 5, 9, 19, 32, 17, 64, 53, 11, 128, 23, 256, 67, 49, 131, 512, 59, 27, 311, 25, 241, 1024, 2048, 31, 719, 83, 4096, 1619, 361, 331, 8192, 227, 16384, 739, 3671, 32768, 277, 81, 103, 2063, 65536, 97, 1523, 2809, 8161, 131072, 262144, 17863

Offset: 1

Author

Gus Wiseman, Sep 06 2018

Keywords

• nonn

Examples

			The sequence of all planted achiral trees begins: o, (o), (oo), ((o)), (ooo), ((oo)), (oooo), (((o))), ((o)(o)), ((ooo)), (ooooo), (((oo))), (oooooo), ((oooo)), ((((o)))), (ooooooo), (((o)(o))), (oooooooo), (((ooo))), ((oo)(oo)).
		

Links

• Gus Wiseman, The first 81 planted achiral trees corresponding to the first 81 dividing partitions.

Crossrefs

Cf. A000040, A001221, A003238, A008480, A061775, A214577, A318990, A318991, A318992.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ptnToAch[y_]:=Fold[Table[#1,{#2}]&,{},Divide@@@Partition[Append[y,1],2,1]];
MGNumber[[]]:=1;MGNumber[x:[__]]:=If[Length[x]==1,Prime[MGNumber[x[[1]]]],Times@@Prime/@MGNumber/@x];
MGNumber/@ptnToAch/@Reverse/@primeMS/@Select[Range[100],Or[#==1,PrimeQ[#],Divisible@@Reverse[primeMS[#]]]&]