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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 January 16 03:17 EST 2019. Contains 319184 sequences. (Running on oeis4.)