A260930 Differences between the numbers n such that n^2 + 2 is prime.

1, 2, 6, 6, 6, 12, 6, 6, 12, 24, 18, 6, 6, 6, 6, 24, 24, 48, 6, 12, 6, 6, 6, 18, 24, 6, 6, 12, 24, 6, 12, 6, 6, 12, 30, 6, 6, 12, 6, 6, 24, 24, 12, 36, 6, 6, 12, 30, 6, 42, 24, 6, 18, 12, 42, 24, 30, 12, 18, 30, 18, 12, 6, 6, 24, 24, 12, 12, 30, 24, 36, 42, 18

Offset: 1

Author

Michel Lagneau, Aug 04 2015

Keywords

• nonn

Comments

Sequence A067201 has the values of n. This sequence is the first differences of A067201.

a(n) is divisible by 6 for n>2.

Examples

			a(6)=12 because A067201(7) - A067201(6) = 33 - 21 = 12.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Cf. A056899 (primes of the form n^2+2), A067201 (values of n).

Programs

Maple

i0:=0:
for k from 1 to 1500 do:
   p:=k^2+2:
   if isprime(p) then printf(`%d, `,k-i0):i0:=k:
   else
   fi:
od:

Mathematica

Differences[Select[Range[1500], PrimeQ[2 + #^2] &, 100]]

PARI

first(m)=my(u=vector(m+1),v=vector(m),r=0);for(i=1,m+1,while(!isprime(r^2 + 2),r++);u[i]=r;r++);for(i=1,m,v[i]=u[i+1]-u[i]);v; \\ Anders Hellström, Aug 14 2015