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

1,2

Links

Table of n, a(n) for n=1..54.

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

Example

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)).

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[#]]]&]

Crossrefs

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

Sequence in context: A365930 A111699 A067179 * A355482 A188843 A209406

Adjacent sequences: A318990 A318991 A318992 * A318994 A318995 A318996

Keyword

nonn

Author

Gus Wiseman, Sep 06 2018

Status

approved