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

1,2

Links

Table of n, a(n) for n=1..30.

Formula

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

Example

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.

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

Crossrefs

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

Sequence in context: A149178 A344559 A318701 * A222506 A108596 A204270

Adjacent sequences: A152913 A152914 A152915 * A152917 A152918 A152919

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 15 2008

Extensions

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

Status

approved