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

Author

Juri-Stepan Gerasimov, Dec 15 2008

Keywords

• nonn

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.
		

Crossrefs

Cf. A000040, A000392, A141468, A152622, A152916.

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