A151990 If p and q are (odd) twin primes and q > p then p*q^2 + (p + q) + 1 is divisible by 6; a(n) = (p*q^2 + (p + q) + 1)/6.

14, 43, 314, 1029, 4655, 12649, 36610, 63084, 178619, 211914, 441209, 566275, 977430, 1185824, 1300299, 1984094, 2313640, 3292695, 3750929, 5078164, 7044274, 12377470, 13468104, 16470839, 23751609, 30919745, 36060100, 39401929

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A164689(n)/2. a(n) = (p+1)*(p^2 + 3p + 3)/6 where p = A001359(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: A151990 := proc(n) p := A001359(n) ; (p+1)*(p^2+3*p+3)/6 ; end: seq(A151990(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)/6];
Array[a, 28] (* Jean-François Alcover, Mar 31 2020 *)
(#[[1]]#[[2]]^2+#[[1]]+#[[2]]+1)/6&/@Select[Partition[Prime[Range[200]], 2, 1], #[[2]]- #[[1]] == 2&] (* Harvey P. Dale, Jul 06 2024 *)

Crossrefs

Cf. A164689.

Sequence in context: A302219 A302665 A041380 * A156166 A064125 A089031

Adjacent sequences: A151987 A151988 A151989 * A151991 A151992 A151993

Keyword

nonn

Author

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

Extensions

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

Status

approved