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

1, 1, 20, 1, 32, 1, 44, 107, 1, 139, 80, 1, 92, 203, 227, 1, 259, 140, 1, 307, 164, 347, 562, 200, 1, 212, 1, 224, 1447, 260, 539, 1, 1157, 1, 619, 643, 332, 683, 707, 1, 1493, 1, 392, 1, 2056, 2176, 452, 1, 464, 947, 1, 1973, 1019, 1043, 1067, 1, 1099, 560, 1, 2309

Offset: 1

Author

Claudio Meller, Jun 26 2009

Keywords

• nonn

Examples

			a(1) = 4-3 = 1;
a(2) = 6-5 = 1;
a(3) = (8+9+10)-7 = 20;
a(4) = 12-11 = 1;
a(5) = (14+15+16)-13 = 32;
a(6) = 18-17 = 1;
a(7) = (20+21+22)-19 = 44;
a(8) = (24+25+26+27+28)-23 = 107; etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A054265, A155752 (n for which a(n)=1).

Programs

Maple

Primes:= select(isprime,[2,seq(i,i=3..1000,2)]):
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

Formula

a(n) = A054265(n+1) - A000040(n+1). - R. J. Mathar, Jun 27 2009

a(n) = (prime(n+2)^2 - prime(n+1)^2 - prime(n+2) - 3*prime(n+1))/2. - Robert Israel, Jul 19 2018

Extensions

Edited and corrected by Robert Israel, Jul 18 2018