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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 *) 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

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Last modified June 4 10:04 EDT 2020. Contains 334825 sequences. (Running on oeis4.)