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%I #25 Mar 15 2024 02:22:33
%S 1,4,10,35,286,969,4495,12341,35990,62196,176851,209934,437989,562475,
%T 971970,1179616,1293699,1975354,2303960,3280455,3737581,5061836,
%U 7023974,12347930,13436856,16435111,23706021,30865405,35999900,39338069
%N Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly two of k, k+1, and k+2 are prime.
%F a(n) = A000292(A124588(n-1)), n > 1. - _R. J. Mathar_, Aug 14 2009
%e k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is in the sequence.
%e k=2: Of the three numbers (2,3,4), exactly two are prime, so 2*3*4/6 = 4 is in the sequence.
%e k=4: Of the three numbers (4,5,6), exactly one is prime, so 4*5*6/6 = 20 is not in the sequence.
%p A000292 := proc(n) n*(n+1)*(n+2)/6; end: for n from 1 to 800 do ps := 0 ; if isprime(n) then ps := ps+1 ; fi; if isprime(n+1) then ps := ps+1 ; fi; if isprime(n+2) then ps := ps+1 ; fi; if ps = 2 then printf("%d,", A000292(n)) ; fi; od: # _R. J. Mathar_, Aug 14 2009
%Y Cf. A000040, A000292, A141468, A144521, A152622.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Dec 15 2008
%E Name and Example section clarified by _Jon E. Schoenfield_, Aug 06 2017
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