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

Author

Olivier Bélot, Jan 20 2017

Keywords

• nonn

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

Examples

			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
		

Links

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

Crossrefs

Cf. A006862, A002110.

Programs

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 *)

Formula

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

Extensions

More terms from Michael De Vlieger, Jan 20 2017