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A280996 Entries are the prime Matula-Goebel numbers of generalized Bethe trees. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also prime numbers p whose index pi(p) is the Matula-Goebel 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 n-th 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: A042989 A302493 A188713 * A089084 A262835 A258261

Adjacent sequences:  A280993 A280994 A280995 * A280997 A280998 A280999

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 12 2017

STATUS

approved

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Last modified November 18 12:35 EST 2019. Contains 329261 sequences. (Running on oeis4.)