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

1,3

Links

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

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

Example

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.

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

Crossrefs

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

Sequence in context: A140116 A084923 A141589 * A040419 A200092 A164812

Adjacent sequences: A162150 A162151 A162152 * A162154 A162155 A162156

Keyword

nonn

Author

Claudio Meller, Jun 26 2009

Extensions

Edited and corrected by Robert Israel, Jul 18 2018

Status

approved