cp's OEIS Frontend

A162153 Differences between the sum of consecutive composites and the prime that precedes them.

%I A162153 #20 Mar 11 2019 09:40:32
%S A162153 1,1,20,1,32,1,44,107,1,139,80,1,92,203,227,1,259,140,1,307,164,347,
%T A162153 562,200,1,212,1,224,1447,260,539,1,1157,1,619,643,332,683,707,1,1493,
%U A162153 1,392,1,2056,2176,452,1,464,947,1,1973,1019,1043,1067,1,1099,560,1,2309
%N A162153 Differences between the sum of consecutive composites and the prime that precedes them.
%H A162153 Robert Israel, <a href="/A162153/b162153.txt">Table of n, a(n) for n = 1..10000</a>
%F A162153 a(n) = A054265(n+1) - A000040(n+1). - _R. J. Mathar_, Jun 27 2009
%F A162153 a(n) = (prime(n+2)^2 - prime(n+1)^2 - prime(n+2) - 3*prime(n+1))/2. - _Robert Israel_, Jul 19 2018
%e A162153 a(1) = 4-3 = 1;
%e A162153 a(2) = 6-5 = 1;
%e A162153 a(3) = (8+9+10)-7 = 20;
%e A162153 a(4) = 12-11 = 1;
%e A162153 a(5) = (14+15+16)-13 = 32;
%e A162153 a(6) = 18-17 = 1;
%e A162153 a(7) = (20+21+22)-19 = 44;
%e A162153 a(8) = (24+25+26+27+28)-23 = 107; etc.
%p A162153 Primes:= select(isprime,[2,seq(i,i=3..1000,2)]):
%p A162153 seq((Primes[i+1]^2-Primes[i+1]-Primes[i]^2-3*Primes[i])/2, i=2..nops(Primes)-1); # _Robert Israel_, Jul 18 2018
%Y A162153 Cf. A000040, A054265, A155752 (n for which a(n)=1).
%K A162153 nonn
%O A162153 1,3
%A A162153 _Claudio Meller_, Jun 26 2009
%E A162153 Edited and corrected by _Robert Israel_, Jul 18 2018