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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 22 15:05 EST 2020. Contains 332137 sequences. (Running on oeis4.)