A129856 Primes that are one less than the difference between consecutive primes.

3, 3, 3, 5, 5, 3, 3, 5, 5, 5, 3, 5, 3, 5, 7, 3, 3, 3, 13, 3, 5, 5, 5, 3, 5, 5, 3, 11, 11, 3, 3, 5, 5, 5, 5, 5, 3, 13, 3, 3, 13, 5, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 5, 3, 5, 7, 3, 3, 11, 7, 3, 7, 3, 5, 11, 17, 5, 5, 5, 5, 5, 5, 5, 5, 3, 11, 3, 5, 5, 11, 3, 5, 7, 7, 7, 5, 5, 3, 7, 5, 3, 7, 3, 13, 11, 3, 13, 3, 3

Offset: 1

Author

Cino Hilliard, May 23 2007

Keywords

• easy
• nonn

Comments

Might be called Prime Prime Intervals: the sequence of prime numbers that occur as 1 less than the difference between consecutive prime numbers. - Barry Forman, Oct 14 2016

Examples

			The first 4 consecutive prime pairs are (2,3),(3,5),(5,7),(7,11). The differences - 1 are the numbers 0,1,1,3. The first three of these are not prime so 3 is the first entry in the table.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

P:= select(isprime, [2,seq(p,p=3..10^4,2)]):
select(isprime, [seq(P[i]-P[i-1]-1,i=2..nops(P))]); # Robert Israel, Apr 18 2016

Mathematica

Select[Last[#]-First[#]&/@Partition[Prime[Range[150]],2,1]-1,PrimeQ] (* Harvey P. Dale, Nov 18 2013 *)

PARI

diffp1p2(n) = { local(p1,p2,y); for(x=1,n, p1=prime(x); p2=prime(x+1); y=(p2-p1)- 1; if(isprime(y), print1(y",") ) ) }