A144521 Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly one of k, k+1, and k+2 is prime.
0, 20, 56, 84, 165, 220, 364, 455, 680, 816, 1140, 1330, 1771, 2024, 2300, 3654, 4060, 4960, 5456, 7770, 8436, 9139, 10660, 11480, 13244, 14190, 16215, 17296, 18424, 23426, 24804, 26235, 32509, 34220, 37820, 39711, 47905, 50116, 52394, 57155
Offset: 1
Keywords
Examples
k=0: Of the three numbers (0,1,2), exactly one is prime, so 0*1*2/6 = 0 is in the sequence. k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is not in the sequence. k=4: Of the three numbers (4,5,6), exactly one is prime, so 4*5*6/6 = 20 is in the sequence.
Programs
-
Maple
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
Extensions
Corrected (455, 14190, 17296 inserted, 16560 removed etc.) by R. J. Mathar, May 01 2010
Name and Example section clarified by Jon E. Schoenfield, Aug 06 2017