A114331 Observe that A052248(n) = greatest prime divisor q (say) of all composite numbers between p = prime(n) and next prime. There is only one composite number in this range which is divisible by q. Sequence lists these composite numbers.

4, 6, 10, 12, 14, 18, 22, 26, 30, 34, 38, 42, 46, 51, 58, 60, 62, 69, 72, 74, 82, 86, 94, 99, 102, 106, 108, 111, 122, 129, 134, 138, 146, 150, 155, 158, 166, 172, 178, 180, 183, 192, 194, 198, 206, 218, 226, 228, 232, 237, 240, 249, 254, 262, 267, 270

Offset

2,1

Comments

The uniqueness follows from generalization of Bertrand's Postulate. - Franklin T. Adams-Watters.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Eric Weisstein's World of Mathematics, Bertrand's Postulate

Maple

p:= 3: R:= NULL:
for i from 2 to 100 do
  pp:= p; p:= nextprime(p);
  rmax:= 0:
  for q from pp+1 to p-1 do
    r:= max(numtheory:-factorset(q));
    if r > rmax then rmax:= r; qmax:= q fi
  od;
  R:= R, qmax
od:
R; # Robert Israel, Apr 01 2021

Crossrefs

Cf. A052248, A114349.

Sequence in context: A199536 A284883 A134333 * A102070 A026402 A036438

Adjacent sequences: A114328 A114329 A114330 * A114332 A114333 A114334

Keyword

nonn

Author

N. J. A. Sloane, based on correspondence from Leroy Quet and Hugo Pfoertner, Feb 22 2006

Status

approved