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 A054265 Sum of composite numbers between successive primes. 15
 0, 4, 6, 27, 12, 45, 18, 63, 130, 30, 170, 117, 42, 135, 250, 280, 60, 320, 207, 72, 380, 243, 430, 651, 297, 102, 315, 108, 333, 1560, 387, 670, 138, 1296, 150, 770, 800, 495, 850, 880, 180, 1674, 192, 585, 198, 2255, 2387, 675, 228, 693, 1180, 240, 2214, 1270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS James Spahlinger, Table of n, a(n) for n = 1..1000 FORMULA a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2, where prime(n) = A000040(n) is the n-th prime. - Zak Seidov, Sep 12 2002 EXAMPLE Between 7 and 11 we have 8 + 9 + 10 which is a(4)=27. MAPLE P:=proc(n) ((ithprime(n+1)-1)*ithprime(n+1)-ithprime(n)*(ithprime(n)+1))/2; end: seq(P(i), i=1..54); # Paolo P. Lava, Apr 27 2018 MATHEMATICA f[n_, x_]:=n*x+x*(x+1)/2; Table[f[Prime[n], Prime[n+1]-Prime[n]-1], {n, 6!}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2010 *) f[n_] := Block[{p0 = Prime[n], p1 = Prime[n + 1]}, (p1 + p0) (p1 - p0 - 1)/2]; Array[f, 54] (* Robert G. Wilson v, Nov 28 2012 *) PROG (PARI) a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2; \\ Michel Marcus, Mar 24 2016 CROSSREFS Cf. A000040, A046933, A054264, A054266, A054267, A054268. Sequence in context: A193689 A099941 A074120 * A105409 A109934 A068321 Adjacent sequences:  A054262 A054263 A054264 * A054266 A054267 A054268 KEYWORD nonn AUTHOR Patrick De Geest, Apr 15 2000 STATUS approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)