

A280996


Entries are the prime MatulaGoebel numbers of generalized Bethe trees.


5



2, 3, 5, 7, 11, 17, 19, 23, 31, 53, 59, 67, 83, 97, 103, 127, 131, 227, 241, 277, 311, 331, 419, 431, 509, 563, 661, 691, 709, 719, 739, 1433, 1523, 1543, 1619, 1787, 1879, 2063, 2221, 2309, 2437, 2897, 3001, 3637, 3671, 3803, 4091, 4637, 4943, 5189, 5381
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OFFSET

1,1


COMMENTS

Also prime numbers p whose index pi(p) is the MatulaGoebel number of a planted achiral tree.
An alternative definition: prime(n) is in the sequence iff n is a perfect power of a prime number already in the sequence.


LINKS

Table of n, a(n) for n=1..51.


FORMULA

a(1) = 2; a(n+1) = prime(A214577(n)).


EXAMPLE

a(n) = prime(Prod_{i in y} a(i)) where y is the nth partition in the following sequence, which spans all constant partitions: 1,2,11,3,4,111,22,5,1111,6,7,8,33,222,9,11111,44,...


MATHEMATICA

nn=10000;
BTQ[n_]:=Or[n===1, MatchQ[PrimePi/@FactorInteger[n][[All, 1]], {_?BTQ}]];
Prime/@Select[Range[PrimePi[nn]], BTQ]


CROSSREFS

Cf. A003238, A214577, A280994, A276625, A277098, A007097.
Sequence in context: A333872 A302493 A188713 * A089084 A262835 A258261
Adjacent sequences: A280993 A280994 A280995 * A280997 A280998 A280999


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 12 2017


STATUS

approved



