login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A144521
Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly one of k, k+1, and k+2 is prime.
1
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
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
KEYWORD
nonn
AUTHOR
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