A152916 Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly two of k, k+1, and k+2 are prime.

1, 4, 10, 35, 286, 969, 4495, 12341, 35990, 62196, 176851, 209934, 437989, 562475, 971970, 1179616, 1293699, 1975354, 2303960, 3280455, 3737581, 5061836, 7023974, 12347930, 13436856, 16435111, 23706021, 30865405, 35999900, 39338069

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 15 2008

Keywords

• nonn

Examples

			k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is in the sequence.
k=2: Of the three numbers (2,3,4), exactly two are prime, so 2*3*4/6 = 4 is in the sequence.
k=4: Of the three numbers (4,5,6), exactly one is prime, so 4*5*6/6 = 20 is not in the sequence.
		

Crossrefs

Cf. A000040, A000292, A141468, A144521, A152622.

Programs

Maple

A000292 := proc(n) n*(n+1)*(n+2)/6; end: for n from 1 to 800 do ps := 0 ; if isprime(n) then ps := ps+1 ; fi; if isprime(n+1) then ps := ps+1 ; fi; if isprime(n+2) then ps := ps+1 ; fi; if ps = 2 then printf("%d,", A000292(n)) ; fi; od: # R. J. Mathar, Aug 14 2009

Formula

a(n) = A000292(A124588(n-1)), n > 1. - R. J. Mathar, Aug 14 2009

Extensions

Name and Example section clarified by Jon E. Schoenfield, Aug 06 2017