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A280996 Prime Matula-Goebel numbers of generalized Bethe trees. 5

%I #13 Nov 04 2023 14:00:22

%S 2,3,5,7,11,17,19,23,31,53,59,67,83,97,103,127,131,227,241,277,311,

%T 331,419,431,509,563,661,691,709,719,739,1433,1523,1543,1619,1787,

%U 1879,2063,2221,2309,2437,2897,3001,3637,3671,3803,4091,4637,4943,5189,5381

%N Prime Matula-Goebel numbers of generalized Bethe trees.

%C Also prime numbers p whose index pi(p) is the Matula-Goebel number of a planted achiral tree.

%C An alternative definition: prime(n) is in the sequence iff n is a perfect power of a prime number already in the sequence.

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

%e 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,...

%t nn=10000;

%t BTQ[n_]:=Or[n===1,MatchQ[PrimePi/@FactorInteger[n][[All,1]],{_?BTQ}]];

%t Prime/@Select[Range[PrimePi[nn]],BTQ]

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Jan 12 2017

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)