A280996 Prime Matula-Goebel numbers of generalized Bethe trees.

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

Offset: 1

Author

Gus Wiseman, Jan 12 2017

Keywords

• nonn

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.

Examples

			a(n) = prime(Product_{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,...
		

Crossrefs

Cf. A003238, A214577, A280994, A276625, A277098, A007097.

Programs

Mathematica

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

Formula

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