A164689 If p and q are (odd) twin primes and q > p then p*q^2+(p+q)+1 is divisible by 3; a(n) = (p*q^2+(p+q)+1)/3.

28, 86, 628, 2058, 9310, 25298, 73220, 126168, 357238, 423828, 882418, 1132550, 1954860, 2371648, 2600598, 3968188, 4627280, 6585390, 7501858, 10156328, 14088548, 24754940, 26936208, 32941678, 47503218, 61839490, 72120200

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = 2*A151990(n). - R. J. Mathar, Sep 18 2009

Maple

A001359 := proc(n) if n = 1 then 3; else for p from procname(n-1)+2 by 2 do if isprime(p) and isprime(p+2) then RETURN(p) ; fi; od: fi; end: A164689 := proc(n) p := A001359(n) ; (p+1)*(p^2+3*p+3)/3 ; end: seq(A164689(n), n=1..80) ; # R. J. Mathar, Sep 18 2009

Mathematica

(* b = A001359 *)
b[n_] := b[n] = If[n == 1, 3, Module[{p = NextPrime[b[n - 1]]}, While[ !PrimeQ[p + 2], p = NextPrime[p]]; p]];
a[n_] := With[{p = b[n]}, (p + 1)(p^2 + 3 p + 3)/3];
Array[a, 27] (* Jean-François Alcover, Mar 31 2020 *)

Crossrefs

Cf. A151990.

Sequence in context: A042540 A042544 A042546 * A096384 A065655 A341623

Adjacent sequences: A164686 A164687 A164688 * A164690 A164691 A164692

Keyword

nonn

Author

Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Aug 22 2009

Extensions

Incorrect leading term deleted by N. J. A. Sloane, Sep 14 2009

More terms from R. J. Mathar, Sep 18 2009

Status

approved