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

1,2

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.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Near-Square Prime

Example

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

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]]

Prog

(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

Crossrefs

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

Sequence in context: A096014 A071888 A117217 * A161331 A120627 A089879

Adjacent sequences: A260927 A260928 A260929 * A260931 A260932 A260933

Keyword

nonn

Author

Michel Lagneau, Aug 04 2015

Status

approved