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A330775 Irregular triangle read by rows: row n gives the primes of the form m*prime(n)+1 where m is an even number <= prime(n) and prime(n) is the n-th prime, or 0 if no such prime exists for any n. 1
5, 7, 11, 29, 43, 23, 67, 89, 53, 79, 131, 157, 103, 137, 239, 191, 229, 47, 139, 277, 461, 59, 233, 349, 523, 311, 373, 683, 149, 223, 593, 1259, 83, 739, 821, 1231, 1559, 173, 431, 947, 1033, 1291, 1549, 1721, 283, 659, 941, 1129, 1223, 1693, 1787, 2069, 107, 743, 1061, 1697, 2333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All safe primes are in this sequence.

Conjecture: For every prime p, there is at least one even m <= p such that m*p+1 is prime.

LINKS

Metin Sariyar, Rows n = 1..220

FORMULA

T(n, 1) = A035095(n) for n>1. - Michel Marcus, Jan 02 2020

EXAMPLE

For n = 4, m = {4, 6}, prime(4) = 7, and 4*7+1 = 29, 6*7+1 = 43 are primes.

Rows of the triangle:

n=1 => {5}

n=2 => {7}

n=3 => {11}

n=4 => {29, 43}

n=5 => {23, 67, 89}

n=6 => {53, 79, 131, 157}

n=7 => {103, 137, 239}

n=8 => {191, 229}

n=9 => {47, 139, 277, 461}

...

MATHEMATICA

row[n_] := Select[2 * Range[Floor[(p = Prime[n])/2]] * p + 1, PrimeQ]; row /@ Range[16] //Flatten (* Amiram Eldar, Jan 02 2020 *)

PROG

(PARI) row(n) = select(x->isprime(x), vector(prime(n)\2, k, 2*k*prime(n)+1)); \\ Michel Marcus, Feb 05 2020

CROSSREFS

Cf. A005384 (Sophie Germain primes), A005385 (safe primes), A035095.

Sequence in context: A057247 A157437 A213677 * A031134 A144231 A050299

Adjacent sequences:  A330772 A330773 A330774 * A330776 A330777 A330778

KEYWORD

nonn,tabf

AUTHOR

Metin Sariyar, Dec 30 2019

STATUS

approved

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Last modified September 23 01:32 EDT 2020. Contains 337291 sequences. (Running on oeis4.)