A260405 Irregular array read by rows, where the n-th row lists the primes p < A002110(n) such that 2*A002110(n) - p is also prime.

5, 7, 13, 17, 19, 23, 29, 11, 19, 23, 31, 37, 41, 47, 53, 61, 67, 71, 73, 83, 89, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 179, 181, 191, 193, 197, 17, 23, 29, 37, 53, 59, 71, 73, 97, 101, 103, 107, 113, 127, 137, 139, 157, 163, 173, 179, 197, 199, 211, 223, 229, 257, 263, 271

Offset: 1

Author

Jean-Marc Rebert, Jul 24 2015

Keywords

• nonn
• tabf

Comments

For each p in row n, (p, 2*A002110(n) - p) is a pair of centered primes at A002110(n) = prime(n)#.

The number of terms in row n are 0, 1, 6, 30, 190, ...; this is A147517.

Examples

			The first row is empty.
T(2,1) = 5 because (5,7) is a pair of primes centered at A002110(2) = prime(2)# = 6.
Triangle starts:
[];
[5];
[7, 13, 17, 19, 23, 29];
[11, 19, 23, 31, 37, 41, 47, 53, 61, 67, 71, 73, 83, 89, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 179, 181, 191, 193, 197];
...
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 1..18866 (the first 7 rows).

Crossrefs

Cf. A000040, A002110, A147517, A260384.

Cf. A260388 (row 3).

Programs

PARI

a147517=[0,1,6,30,190,1564,17075,226758,3792532]
a002110(n)=prod(i=1, n, prime(i))
a(n)=my(k=2,maxk=2,primorielle=2,s=0,y=5);if(n==1, y=5, maxk=2;while(sum(k=2, k=maxk, a147517[k])
				

PARI

row(n) = {v = []; pn = prod(i=1, n, prime(i)); forprime(p=1, pn-1, if (isprime(2*pn-p), v = concat(v, p))); v;} \\ Michel Marcus, Aug 02 2015

PARI

a002110(n) = prod(p=1,n,prime(i));
T(n,k) = my(P= a002110(n),compteur = 0,q=0,y=-1);forprime(p=1,P-1,q = 2*P-p;if(isprime(q),compteur++;if(compteur== k,y=p;y;break)));y