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%I #11 Aug 07 2017 04:53:07
%S 0,20,56,84,165,220,364,455,680,816,1140,1330,1771,2024,2300,3654,
%T 4060,4960,5456,7770,8436,9139,10660,11480,13244,14190,16215,17296,
%U 18424,23426,24804,26235,32509,34220,37820,39711,47905,50116,52394,57155
%N Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly one of k, k+1, and k+2 is prime.
%e k=0: Of the three numbers (0,1,2), exactly one is prime, so 0*1*2/6 = 0 is in the sequence.
%e k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is not in the sequence.
%e k=4: Of the three numbers (4,5,6), exactly one is prime, so 4*5*6/6 = 20 is in the sequence.
%p isPr := proc(n) if isprime(n) then 1; else 0; end if; end proc: for n from 0 to 300 do if isPr(n)+isPr(n+1)+isPr(n+2) = 1 then printf("%d,",n*(n+1)*(n+2)/6 ) ; end if; end do: # _R. J. Mathar_, May 01 2010
%Y Cf. A000040, A000392, A141468, A152622, A152916.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Dec 15 2008
%E Corrected (455, 14190, 17296 inserted, 16560 removed etc.) by _R. J. Mathar_, May 01 2010
%E Name and Example section clarified by _Jon E. Schoenfield_, Aug 06 2017