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

1,1

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.

Links

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

Example

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];
...

Prog

(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])<n, maxk++; s=sum(k=2, k=maxk, a147517[k-1])); k=maxk; primorielle=a002110(k); forprime(p=2, primorielle, if(isprime(2*primorielle-p), s++; if(s==n, y=p; break))); return(y); )
(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

Crossrefs

Cf. A000040, A002110, A147517, A260384.

Cf. A260388 (row 3).

Sequence in context: A259542 A236204 A152810 * A108719 A162707 A216769

Adjacent sequences: A260402 A260403 A260404 * A260406 A260407 A260408

Keyword

nonn,tabf

Author

Jean-Marc Rebert, Jul 24 2015

Status

approved