A129856 - OEIS

%I #33 Jan 07 2025 10:52:25

%S 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,

%T 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,

%U 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

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

%C 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

%H Robert Israel, <a href="/A129856/b129856.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p P:= select(isprime, [2,seq(p,p=3..10^4,2)]):

%p select(isprime, [seq(P[i]-P[i-1]-1,i=2..nops(P))]); # _Robert Israel_, Apr 18 2016

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

%o (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",") ) ) }

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 23 2007