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

1,1

Comments

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

Links

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

Cino Hilliard, Frequency of primes.

Example

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

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 *)

Prog

(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", ") ) ) }

Crossrefs

Sequence in context: A083574 A108025 A192451 * A136800 A126661 A369859

Adjacent sequences: A129853 A129854 A129855 * A129857 A129858 A129859

Keyword

easy,nonn

Author

Cino Hilliard, May 23 2007

Status

approved