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A339414 Primes p such that (p+q)/4 is prime, where q is the next prime after p. 2
3, 5, 23, 31, 83, 131, 251, 271, 331, 383, 443, 563, 971, 1123, 1223, 1231, 1283, 1291, 1543, 2063, 2371, 2383, 2551, 2851, 2903, 2963, 3083, 3323, 3691, 3889, 4051, 4283, 4591, 4733, 4831, 4871, 4951, 5003, 5209, 5351, 5683, 5711, 5851, 6229, 6271, 6323, 6491, 6863, 6911, 7393, 7451, 7583, 7643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

After the initial 2 terms, a(n)=2*A118134(n)-3. - Hugo Pfoertner, Dec 03 2020

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5)=83 is in the sequence because it is prime, the next prime is 89, and (83+89)/4 = 43 is prime.

MAPLE

P:= select(isprime, [seq(i, i=3..10000, 2)]):

R:= (P[1..-2]+P[2..-1])/4:

P[select(i-> R[i]::integer and isprime(R[i]), [$1..nops(R)])];

PROG

(PARI) isok(p) = isprime(p) && iferr(isprime((p+nextprime(p+1))/4), E, 0); \\ Michel Marcus, Dec 04 2020

CROSSREFS

Subset of A098058.

Cf. A118134.

Sequence in context: A106307 A106282 A163153 * A238199 A296927 A215132

Adjacent sequences:  A339411 A339412 A339413 * A339415 A339416 A339417

KEYWORD

nonn

AUTHOR

Robert Israel, Dec 03 2020

STATUS

approved

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Last modified April 15 10:27 EDT 2021. Contains 342977 sequences. (Running on oeis4.)