Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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