A281318 Number of consecutive nonprime numbers following Euclid numbers A006862.

1, 3, 5, 11, 21, 15, 17, 21, 35, 59, 65, 59, 69, 45, 105, 57, 59, 107, 87, 101, 77, 149, 195, 99, 101, 231, 221, 125, 221, 189, 161, 227, 641, 237, 155, 165, 437, 237, 197, 189, 197, 381, 231, 749, 311, 771, 605, 311, 381, 291, 441, 329, 281, 275, 269, 399

Offset

1,2

Comments

For n > 1, a(n) >= prime(n), with equality if and only if A006862(n) + prime(n) + 1 is prime. Equality occurs for n=2, 3, 7, 17. Are there any others? - Robert Israel, Jan 30 2017

Links

Robert Israel, Table of n, a(n) for n = 1..469

Formula

NextPrime[pn# + 1] - pn# - 1

Example

a(3) = 5 because primorial p_3# = 5# = 2*3*5 = 30 thus 31 is the third Euclid number, and there are 5 consecutive nonprime numbers {32,33,34,35,36} between 31 and the next prime, 37. - Michael De Vlieger, Jan 20 2017

Maple

p:= 0: pn:= 1:
for n from 1 to 100 do
  p:= nextprime(p);
pn:= pn*p;
A[n]:= nextprime(pn+1)-(pn+2);
od:
seq(A[n], n=1..100); # Robert Israel, Jan 30 2017

Mathematica

Table[Function[p, NextPrime@ p - p - 1][Times @@ Prime@ Range@ n + 1], {n, 56}] (* Michael De Vlieger, Jan 20 2017 *)

Crossrefs

Cf. A006862, A002110.

Sequence in context: A339006 A247353 A293948 * A082713 A074710 A057460

Adjacent sequences: A281315 A281316 A281317 * A281319 A281320 A281321

Keyword

nonn

Author

Olivier Bélot, Jan 20 2017

Extensions

More terms from Michael De Vlieger, Jan 20 2017

Status

approved