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

1,2

Links

Table of n, a(n) for n=1..40.

Example

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.

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

Crossrefs

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

Sequence in context: A108108 A316935 A123456 * A044122 A044503 A344072

Adjacent sequences: A144518 A144519 A144520 * A144522 A144523 A144524

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 15 2008

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

Status

approved