A364530 a(n) is the least positive k such that for each of the first 2*n primes p, at least one of the n consecutive integers k to k + n - 1 is divisible by p.

6, 14, 154, 1273, 986, 60605, 138411, 587074, 11682411, 53882397, 1419040497, 10970441168, 162901726271, 162901726270, 14028069972496, 418009365630087, 29188950975317201, 386792219894091763, 3445270276615037892

Offset

1,1

Comments

a(17) <= 29188950975317201. - Martin Ehrenstein, Aug 05 2023

a(20) > 1.8*10^19. - Jon E. Schoenfield, Aug 21 2023

Links

Table of n, a(n) for n=1..19.

Michael Hardy et al., Unusual clump of small prime numbers?, Math Overflow.

Example

a(3) = 154 because each of the first 6 primes 2, 3, 5, 7, 11 and 13 divides at least one of the 3 consecutive numbers 154, 155, 156 (as 2, 7 and 11 divide 154, 5 divides 155, and 2, 3 and 13 divide 156), and 154 is the smallest positive integer that works.

Maple

f:= proc(n) local P, x, p, i;
  P:= select(`>`, [seq(ithprime(i), i=2*n..1, -1)], n);
  x:= 1;
  do
    flag:= true;
    for p in P while flag do
      q:= -x mod p;
      if q >= n then x:= x + q-n+1; flag:= false fi;
    od;
    if flag then return x fi;
  od
end proc:
map(f, [$1..11]);

Crossrefs

Sequence in context: A308489 A301425 A077401 * A263695 A158965 A284075

Adjacent sequences: A364527 A364528 A364529 * A364531 A364532 A364533

Keyword

nonn,more

Author

Robert Israel, Jul 27 2023

Extensions

a(12)-a(15) from Jon E. Schoenfield, Jul 28 2023

a(16) from Martin Ehrenstein, Aug 04 2023

a(17)-a(19) from Jon E. Schoenfield, Aug 20 2023

Status

approved