This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152916 #25 Mar 15 2024 02:22:33
%S A152916 1,4,10,35,286,969,4495,12341,35990,62196,176851,209934,437989,562475,
%T A152916 971970,1179616,1293699,1975354,2303960,3280455,3737581,5061836,
%U A152916 7023974,12347930,13436856,16435111,23706021,30865405,35999900,39338069
%N A152916 Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly two of k, k+1, and k+2 are prime.
%F A152916 a(n) = A000292(A124588(n-1)), n > 1. - _R. J. Mathar_, Aug 14 2009
%e A152916 k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is in the sequence.
%e A152916 k=2: Of the three numbers (2,3,4), exactly two are prime, so 2*3*4/6 = 4 is in the sequence.
%e A152916 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 A152916 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 A152916 Cf. A000040, A000292, A141468, A144521, A152622.
%K A152916 nonn
%O A152916 1,2
%A A152916 _Juri-Stepan Gerasimov_, Dec 15 2008
%E A152916 Name and Example section clarified by _Jon E. Schoenfield_, Aug 06 2017